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VERS11Y  OF  tTALlFORNIA, 


ANGELE; 


S1TY  of 
AT 
U)S 


MODERN  HARMONY 


IN  ITS 


BY 

ARTHUR  FOOTE  A.M. 


WALTER  R.  SPALDING  A.M. 

Assistant  Professor  of  Music  at  Harvard  University 


PRICE  $1.50 


ARTHUR-  P.- SCHMIDT  •.- 

BOSTON  LEIPZIG  NEW  YORK 

120  BOVLSTON  STREET  130  FIFTH  AVENUE 

Copyright  1905  by  AKTHUH  P.  SCHMIDT 


2813 


700  *l 


MUSIC 

LIBUMN 


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73 


PEEFAOE 


THE  title  of  this  work  indicates  the  aim  of  the  authors.  Not  a  few 
statements  and  rules  have  been  current  in  text-books  that,  from  the  point 
of  view  of  composers  and  of  the  best  teachers  to-day,  are  unnecessary  and 
sometimes  even  incorrect.  When  we  find  a  rule  constantly  broken  by  one 
great  composer  after  another,  it  is  probable  that  the  rule  ought  to  be  mod- 
ified or  given  up,  and  not  that  the  composers  are  wrong.  It  is  the  inten- 
tion that  statements  and  rules  in  this  book  shall  be  expressed  with  exact 
truth,  and  explained  when  real  explanation  is  possible.  It  has  also  been 
remembered  that  better  work  is  secured  by  directions  as  to  what  may  be 
done,  than  by  laying  too  much  stress  upon  what  is  forbidden. 

About  some  matters  there  is  a  marked  difference  of  opinion  among 
theorists;  such  things  cannot  be  considered  as  settled  for  good  and  all,  and 
no  definite  statement  should  be  made  excluding  other  well-grounded  points 
of  view,  e.g.  the  chords  of  the  llth  and  13th. 

The  chord  of  the  6th  has  been  treated  with  more  detail  than  usual, 
an  attempt  having  been  made  to  analyze  and  classify  the  features  that 
make  this  chord  so  difficult  for  the  student. 

While  the  old  strict  rules  as  to  secondary  7ths  are  given  fully,  the 
modern  theory  and  use  of  these  chords  have  received  just  consideration. 

The  chord  of  the  9th  has  been  discussed  as  a  largely  independent  chord : 
it  was  also  obvious  that  the  growing  feeling  about  chords  of  the  llth  and 
13th  ought  to  be  recognized,  although  the  opinion  of  the  authors,  as  ex- 
plained in  the  chapter  on  that  subject,  is  that  these  latter  can  seldom  be 
classified  as  independent  chords. 

It  is  believed  that  the  treatment  of  chromatic  alterations  in  chords, 
and  of  the  augmented  6th,  6-5  and  6-4-3  chords  is  in  accordance  with 
present  thought,  and  that  this  is  also  the  case  as  regards  suspension. 

The  chapter  on  the  old  modes  is  necessarily  brief,  but  it  is  hoped  that 
it  may  lead  the  student  to  further  investigation  of  an  important  and  inter- 
esting question. 

It  is  often  the  case  that  exercises  with  figured  basses  are  written 
correctly,  but  only  mathematically,  by  simply  reckoning  each  chord  as  a 
kind  of  puzzle,  without  reflecting  that  the  whole  thing  means  music  after 


PREFACE 

all.  The  most  difficult  thing,  for  one  not  used  to  it,  is  the  having  a  mental 
conception  of  the  real  sounds  of  the  symbols  written  down  —  in  other 
words,  hearing  with  the  eye.  Education  now  is  directed  to  the  thing,  not 
to  the  symbol.  As  the  practical  way  of  working  in  that  direction,  in  this 
book  from  the  very  beginning  the  harmonizing  of  melodies  goes  step  by 
step  with  the  writing  from  figured  basses.  It  is  hoped  that  the  illustra- 
tions quoted  from  many  composers  will  be  of  help  by  showing  what  has 
actually  been  done  with  our  harmonic  material. 

For  matters  connected  with  acoustics  (§§  5, 13),  the  student  is  referred 
to  Helmholtz's  book  "On  the  Sensations  of  Tone,"  and  to  the  essay  on 
*'  Partial  Tones"  in  Grove's  "  Dictionary  of  Music." 

BOSTON,  August,  1905. 


TABLE   OF   CO^TTE^TS 


CHAPTER  PAGE 

I  INTERVALS 1 

Consonance  and  dissonance,  7;  Inversion,  9. 

II  THE  SCALES 11 

Circles  of  5ths,  13;  Relative  minor,  15;  Chromatic,  16;  Tonic, 
etc.,  17. 

III  TRIADS 18 

Chord  denned,  18;  Doubling  of  intervals,  19;  Open  and  close 
position,  20;  Similar  motion,  etc.,  22;  Consecutive  8ves  and 
5ths,  24;  Voice-leading,  27;  Leading-tone,  28;  Rules  for  triads, 
29. 

IV  EXERCISES  WITH  TRIADS  IN  MAJOR  KEYS 31 

Directions  as  to  figured  basses,  etc.,  31 ;  Exercises,  34. 

V  EXERCISES  IN  HARMONIZING  SOPRANO  MELODIES 36 

Triad  successions  in  major  keys,  36;  Exercises,  37. 

VI  TRIADS  IN  M:NOR  KEYS 38 

Additional  rules,  39;  Tierce  de  Picardie,  42;  Triad  successions  in 
minor  keys,  43 ;  Three- voice  writing,  43. 

VII   EXERCISES  WITH  TRIADS  IN  MINOR  KEYS 44 

VIII   HIDDEN  SVES  AND  STHS 47 

IX  INVERSIONS  OF  TRIADS 49 

X  CHORD  OF  THE  6TH 50 

Doubling  of  bass  with  single  chords  of  the  6th  in  major  keys,  51 ; 
in  minor  keys,  53. 

XI   CHORDS  OF  THE  6rH  IN  SUCCESSION 54 

General  directions  as  to  doubling  the  bass,  57. 

XII  THE  6-4  CHORD 57 

As  a  passing  chord,  59;  In  succession,  60. 

XIII  EXERCISES  WITH  6  AND  6-4  CHORDS 61 

Harmonizing  melodies,  63;  Three- voice  writing,  65. 

XIV  CADENCES 66 

XV  SEQUENCES     69 

Writing  on  four  staves,  71. 

XVI  CHORDS  OF  THE  7TH 71 

Resolution  defined,  72;  Dominant  7th,  72;  Its  resolution  ex- 
plained, 73;  Rules,  75;  Its  entrance,  76. 

XVII    PASSING  AND  AUXILIARY  TONES 76 

v 


vi  TABLE  OF  CONTENTS 

CHAPTER  PAOK 

XVIII  EXERCISES  WITH  CHORDS  OF  THE  DOMINANT  ?TH 78 

Deceptive  resolution,  79;  Three- voice  writing,  80. 

XIX   INVERSIONS  OF  THE  DOMINANT  7TH 83 

XX  SOME  SIMPLE  MODULATIONS 84 

XXI   EXERCISES  WITH  DOMINANT  7TH  CHORDS  AND  THEIR  INVER- 
SIONS  .    .  ^ 86 

Three-voice  writing,  89. 

XXII   IRREGULAR  RESOLUTIONS  OF  THE  DOMINANT  7TH 93 

XXIII  EXERCISES  WITH  THE  SAME 100 

XXIV  IRREGULAR  RESOLUTIONS  OF  INVERSIONS  OF  THE  DOMINANT  7TH  105 

Allowable  consecutive  Stlis,  106. 
XXV  EXERCISES:    IRREGULAR    RESOLUTIONS   OF    DOMINANT    7TH 

CHORDS  AND  THEIR  INVERSIONS 110 

XXVI   LEADING-TONE   CHORDS    OF  THE  7TH  IN  MAJOR  KEYS  ...     114 

XXVII   EXERCISES  WITH  THE  SAME 117 

XXVIII   LEADING-TONE   CHORDS  OF  THE  7TH  IN  MINOR  KEYS  (DIMIN- 
ISHED 7TH  CHORDS) 120 

Enharmonic  notation,  122;  Consecutive  diminished  7th 
chords,  122;  Cross- relation,  124. 

XXIX   EXERCISES  WITH  THE  SAME 124 

XXX  SECONDARY  CHORDS  OF  THE  7TH 128 

Free  treatment,  129;  The .  strict  rules,  132;  Irregular 
resolutions,  134;  In  succession,  136;  Accented  passing-tone, 
138. 

XXXI  EXERCISES  WITH  SECONDARY  7TH  CHORDS 138 

XXXII  INVERSIONS  OF  SECONDARY  7'rn  CHORDS 142 

XXXIII  EXERCISES  WITH  THE  SAME 146 

XXXIV  CHORDS  OF  THE  9rH 152 

The  C  clefs,  152;  Dominant  9th,  154;  Dominant  9th  with 
root  omitted,  157;  Inversions  of  Dominant  9th,  161; 
Chords  of  the  9th  on  other  degrees  of  the  scale,  161. 

XXXV   EXERCISES  WITH  CHORDS  OF  THE  9rn 163 

XXXVI  CHORDS  OF  THE  HTH  AND  13TH 166 

XXXVII  CHROMATICALLY  ALTERED  CHORDS 171 

Neapolitan  6th,  176. 

XXXVIII   EXERCISES  WITH  ALTERED  CHORDS 179 

XXXIX   AUGMENTED  CHORDS 182 

Augmented   6th,   183;  Augmented  6-4-3,   186;  Augmented 

6-5,  189. 

XL   EXERCISES  WITH  AUGMENTED  CHORDS  AND  THEIR  INVERSIONS.     194 
Three- voice  writing,  198. 

XLI  SUSPENSIONS 199 

XLII   EXERCISES  WITH  SUSPENSIONS 212 

XLIII   ORNAMENTAL  TONES 217 

Passing-tones;  Auxiliary-tones;  Changing-tones ;  Appoggia- 
turas;  Anticipation;  Figuration. 


TABLE   OF   CONTENTS  yii 

CHAPTER  PAGB 
XLIV  EXERCISES  INTRODUCING  ORNAMENTAL  TONES  AND  SUSPEN- 
SIONS     224 

XLV  MODULATION 227 

Table  of  modulations,  230 ;  Changes  of  key  without  modula- 
tion, 234;  Enharmonic  changes  of  key,  235. 

XL VI  EXERCISES  IN  MODULATION 237 

XLVII  CROSS-RELATION 239 

XLVIII   SUGGESTIONS  TO  AID  IN  REVIEWING 241 

XLIX  THE  PEDAL 243 

Exercises,  247. 

L  THE  OLD  MODES 249 

Harmony  other  than  with  four  voices,  252. 


HARMONY 


CHAPTER  I 


-2-  -2.  -2. 
INTERVALS 

0 

1.  THE  study  of  Harmony  —  the  Grammar  of  Music  —  begins  with 
the  subject  of  Intervals,  for  as  soon  as  we  consider  even  two  different  tones 
there  must  be  some  method  of  determining  their  relationship.     An  Interval 
is  the  measurement  of  the  difference  in  pitch  between  any  two  tones,  whether 
they  are  sounded  together  and  stand  in  a  harmonic  relationship,  or  in 
succession  and  are  used  melodically. 

2.  Notes  refer  to  the  written  symbols  —  the  notation  of  music  —  and 
are  apprehended  by  the  eye  ;  tones  refer  to  sounds,  which  must  be  accurately 
determined  and  keenly  felt  by  the  ear.     A  careful  study  of  intervals  helps 
greatly  toward  the  acquisition  of  that  clearness  of  thought  and  cooperation 
of  eye  and  ear  absolutely  indispensable  to  the  well-trained  musician. 

3.  Every  interval  has  a  two-fold   name,  general  and  specific;  i.e.  an 
interval  is  a  third,  a  fourth,  a  fifth,  etc.,  and  also  a  third,  a  fourth,  or  a 
fifth,  of  a  certain  kind;  e.g.  a  major  third,  a  perfect  fourth,  a  diminished 
fifth,  etc. 

4.  The  general  numerical  name  of  an  interval  is  always  determined 
by  counting  inclusively,  from  the  lower  note  to  the  higher,  the  number  of 
lines  and  spaces  involved.     As  lines  and  spaces   (the  scale-degrees)   are 
designated  by  the  letters  of  the  alphabet  from  A  to  G  in  order,  a  simple 
rule  is  this:  —  Always  reckon  intervals  by  letters.     The  interval  C-E  is  always 
a  third,    there   being  three  degrees    (C,  D,  E),   no   matter  how  either  C 
or  E  may  be  qualified  by  accidentals  (sharps,  flats,  and  naturals).1     The 
following  intervals,  for  instance,  are  all  thirds: 


II 


*->         19-  ~#- 

although   not  all   of  the  same  kind.     Likewise  C-F#  is  a  certain  kind  of 
fourth  (C,  D,  E,  F);  C-G*  a  certain  kind  of  fifth  (C,  D,  E,  F,  G). 


1  The  sign  Q  ought  logically  to  be  called  a  cancel,  as  its  office  in  exclusively  to  cancel 
the  sharp  or  flat  that  would  otherwise  be  in  force. 


A.  P.  8.  6904.  Copyright,  1905,  by  Aiiriiru  P.  SciIMlDT.  " 

1 


2  HARMONY 

6.  Exactness  in  thinking  and  writing  intervals  is  of  the  utmost  con- 
sequence, for  it  is  the  same  thing  as  spelling  words  correctly;  moreover 
we  shall  find  later  that  different  intervals  have  different  resolutions,  the 
chords  of  which  they  form  a  part  being  different,  e.g. 


i 


» 


r  -T 


Most  persons  have  only  such  a  conception  of  intervals  as  is  derived  from 
familiarity  with  the  pianoforte  keyboard,  the  result  being  often  an  en- 
tirely wrong  way  of  looking  at  the  matter.  Since  for  practical  reasons 
there  is  but  one  key  of  the  pianoforte  for  both  F$  and  Gt>,  it  at  first 
naturally  seems  that  the  notes  F$  and  Gl?  must  be  identical,  while  really 
they  differ  in  pitch,  when  played  in  perfect  tune  on  a  stringed  instrument. 
This  can  be  perceived  by  an  acute  ear,  if  the  two  tones  are  sounded  simul- 
'ta,neously;  F$  is  higher  in  pitch  than  Gt>  by  a  very  small  interval  called 
the  "Comma  of  Pythagoras,"  which  is  about  one  quarter  of  a  semitone. 
Tones  which  differ  in  notation,  but  sound  alike  on  a  keyed  instrument, 
are  said  to  have  an  enharmonic  relationship. 


DVOBAK,  Requiem 


8.  The  general  kind  of  any  interval  being  thus  determined  by  counting 
the  number  of  letters  in  their  order,  we  must  next  find  what  is  its  specific 
name.  For  this  purpose  intervals  are  classified  as  Perfect,  Major,  Minor, 
Augmented,  and  Diminished.  (In  chromatically  altered  chords,  doubly  aug- 
mented and  doubly  diminished  intervals  are  also  found.)  The  need  for 
these  more  precise  definitions  will  be  clearly  seen  if,  before  going  further, 
we  examine  for  a  moment  the  modern  scale-system. 


HARMONY  3 

7.  A  scale  consists  of  a  succession  of  tones  arranged  according  to  a 
definite  plan.1  Our  major  diatonic  scale,  for  instance,  is  a  succession  of 
seven  different  tones  (hence  called  a  heptatonic  scale),2  so  arranged  that 
between  any  two  degrees  there  is  always  a  whole  tone,  with  the  exception 
of  the  interval  between  the  third  and  fourth,  where  there  is  a  semitone 
(also  between  the  seventh  and  eighth  (or  8ve.)). 

octave 


«^        -&-        ** 

It  will  be  seen  that  the  eighth  tone  or  octave  is  merely  a  repetition  of  the 
first  one  at  a  different  pitch;  at  this  octave  the  series  recommences.  The 
term  "diatonic"  means  throughout  the  tones,  or  degrees,  of  the  scale;  hence 
a  diatonic  scale  is  one  in  which  there  is  one  note,  neither  more  nor  less, 
on  each  degree  of  the  staff,  i.e.  on  each  line  and  space  in  succession.3 
Every  musical  person  has  received  this  succession  of  tones  as  part  of  his 
musical  inheritance,  i.e.  he  can  sing  it  without  effort  when  asked,  and 
readily  recognizes  it  when  heard. 

8.  If  the  intervals  of  the  above  scale  be  examined,  it  is  evident  that 
those  which  have  the  same  general  name  are  not  always  of  the  same  size 
and  by  no  means  of  the  same  effect:  for  instance,  the  intervals  C-E  and 
A-C  are  both  thirds,  but  of  a  different  variety.  If  the  tones  C,  E  are 
sounded  several  times; 


1  If  it  were  not  for  the  traditional  and  convenient  arrangement  of  keys  on  the  piano- 
forte keyboard,  we  should  probably  have  at  least  nineteen  keys  in  an  octave  —  c,  c$,  db, 
d,  dj,  eb,  e,  ef,  f,  f$,  gb,  g,  g&  ab,  a,  aS,  bb,  b,  bfc  —  instead  of  the  tu-eh-e  black  and  white 
keys.  Violinists  have  to  do  with  all  these  tones  in  practical  playing.  Many  compositions  of 
imperfectly  educated  writers  are  defaced  by  a  kind  of  misspelling  which  comes  from  ignor- 
ance of  intervals;  the  student  should  feel  it  to  be  of  equal  importance  to  spell  both  music  and 
language  correctly. 

:  During  the  evolution  of  music  many  kinds  of  scales  have  been  in  use  among  different 
nations,  some  of  which  we  shall  mention  later. 

3  It  is  well  to  realize  this,  for  we  often  find  the  Pentatonic  scale  of  five  tones,  which  ia 
not  a  diatonic  scale,  but  contains  steps  of  more  than  a  tone,  e.g. 


The  student  can  invent  melodies  based  on  this  scale   by  using  the  black  keys  of  the  piano- 
forte. 


4  HARMONY 

and  then,  after  a  pause,  the  notes 


every  one  will  feel  the  striking  difference  between  these  thirds.  The  interval 
A-C  is  called  a  minor  or  lesser  third  (containing  a  tone  and  a  half)  in  com- 
parison with  the  interval  C-E,  which  is  a  major  or  greater  third  (containing 
two  whole  tones).  Of  the  seven  seconds  contained  within  the  scale,  five 
are  major  (containing  one  whole  tone),  C-D,  D-E,  etc.,  whereas  two  are 
minor  (containing  a  semitone),  E-F  and  B-C.  Likewise  in  regard  to  the 
other  intervals:  C-F  is  one  kind  of  a  fourth,  and  F-B  is  another;  the  sixth 
C-A  is  larger  than  the  sixth  E-C;  the  seventh  C-B  sounds  very  different 
from  the  seventh  D-C. 

9.  From  the  above  considerations  it  is  evident  that  the  classification 
of  intervals  as  seconds,  thirds,  fifths,  etc.,  is  not  sufficient;  there  must  be 
some  more  precise  nomenclature  to  show  their  exact  nature,  i.e.  what 
kind  of  a  second,  third,  etc.  In  learning  to  apply  the  specific  terms,  Perfect, 
Major,  Minor,  Augmented,  and  Diminished,  the  easiest  way  to  begin  is  to 
recognize  this  fact :  —  that  in  every  major  scale  the  intervals  having  the 
tonic  (key-note)  for  their  lowest  tone  are  either  major  or  perfect,  e.g. 

Perfect    Malor    Major    Perfect    Perfect    Major    Maior    Perfect 
unison.  1     '><!.          3d.          4th.  5th.         6th.         7th.      octave. 


II 


' -Q©- f3&-       -&-          -Gt-  -lS>-  -&-          -&-  -t 

10.  Minor  intervals,  as  may  be  inferred  from  the  name,  are  a  semitone 
/smaller  than  their  corresponding  majors.  A  major  interval  is  changed  into 
a  minor  either  by  raising  the  lower  note,  or  by  lowering  the  upper  one  a 
chromatic  *  semitone.  Thus  C-E  is  a  major  third;  C$-E  and  C-Eb  are  both 
minor  thirds.  In  forming  minor  thirds  be  sure  that  the  general  interval 
of  a  third  is  preserved.  C-D$, 


for  instance,  as  the  notes  are  on  adjacent  degrees,  is  not  a  third  at  all,  but 
a  second. 

1  The  unison  (two  voices  singing  the  same  tone)  cannot  strictly  b«  called  an  interval, 
but  for  convenience  is  so  named.  When  one  of  its  tones,  however,  is  raised  or  lowered  chro- 
matically, we  do  get  a  real  interval. 

*  A  chromatic  semitone  is  one  in  which  both  notes  are  on  the  same  degree  of  the  staff, 
e.g.  C-CJ;  a  diatonic  semitone  one  between  notes  on  adjoining  degrees,  e.g.  C-B  or  C-D?. 


HARMONY 


(Minor  2ds.        |    Minor  3ds.  I  Minor  6ths.        I  Minor  7ths.          I  Minor  9ths. 


11.  An  augmented  interval  is  a  chromatic  semitone  larger  than  a  per- 
fect or  a  major  interval.  It  is  obvious  that  an  interval  may  be  augmented 
;  either  by  raising  the  upper  note  or  by  lowering  the  lower.  Thus  D-G  being 
a  perfect  fourth,  either  J)-G$  or  Dfr-G  will  be  an  augmented  fourth.  The 
augmented  intervals  starting  on  C  are  as  follows: 


These  augmented  intervals  are  all  usable;  augmented  4ths,  5ths,  6ths,  and, 
in  a  somewhat  less  degree,  2ds,  are  of  frequent  appearance  in  harmony. 
Augmented  3ds,  7ths,  and  8ves  have  no  harmonic  value,  although 
occasionally  found  as  passing  tones,  e.g. 


12.  A  diminished  interval  is  a  chromatic  semitone  less  than  a  perfect 
or  a  minor.  As  in  the  cases  given  above,  it  is  immaterial  which  of  the 
two  tones  composing  the  original  interval  be  altered ;  e.g.  C-G  being  a  per- 
fect 5th,  either  C$-G  or  C-Gb  is  a  diminished  fifth.  The  diminished 
intervals  are: 


If       If      If     If 


a  diminished  unison  is  unthinkable,   and  the  diminished  2d  and  9th  are 
of  no  practical  use: 


in  the  diminished  6th,  the  lower  tone  may  occur  as  a  passing  tone;  e.g. 


• 

s 


Diminished  3ds,  4ths,  Sths,1  and  7ths,  especially  the  last,  occur  frequently 
and  are  of  great  harmonic  use. 

13.  From  the  above  illustrations  it  will  be  seen  that  major  and  minor, 
augmented  and  diminished   intervals  explain  themselves  and  are  readily 
understood.    The  student,  however,  is  often  at  a  loss  to  appreciate  the 
appropriateness  of  the  term  perfect,  as  applied  to  unisons,  4ths,  5ihs,  and 
jjves,  and   to  these  only.     To  most  hearers  the  3d  is  probably  the  most 

,  satisfactory  of  all  intervals  when  sounded  alone,  and  yet  we  are  told  that 
it  is  not  perfect,  while  the  4th  is  called  by  that  name,  although  much  less 
agreeable  by  itself  than  the  third.  These  perfect  intervals  have  been  given 
that  name  to  distinguish  them  from  the  others,  and  for  certain  reasons  in 
acoustics  (the  ratio  of  vibration,  for  example,  in  each  case  is  very  simple, 
and  practically  invariable).  The  perfect  octave  above  any  tone  always 
has  just  twice  the  number  of  vibrations  in  the  same  time  as  that  tone;  i.e. 
the  ratio  of  the  interval  of  the  perfect  octave  is  1:2,  whereas  major  and 
minor  thirds  and  sixths,  as  the  student  will  understand  more  clearly,  when 
he  comes  to  know  about  equal  temperament  and  methods  of  tuning,  have 
not  such  simple  ratios,  and  often  vary  considerably  in  character.  These 
perfect  intervals  also  differ  from  all  the  others  in  that  they  remain  perfect 
when  inverted  (as  will  be  seen  later). 

14.  Before  explaining  Inversions  it  will  be  necessary  to  define  and 
explain  two  terms  of  great  significance  in  the  classification  of  intervals. 

>  A  diminished  interval  when  made  still  smaller  by  a  semitone,  becomes  doubly  dimin- 
ithed;  e.g. 

FKAXZ.  (Song) 


In  like  manner  an  augmented  interval  becomes  doubly  augmented  when  made  a  semi- 
tone larger;  e.g. 


These  intervals  are  not  available  in  simple  chord-formations. 


HARMONY  7 

These  terms  are  Consonance  and  Dissonance,  and  from  the  outset  the 
student  should  have  a  broad  idea  of  their  meaning.  We  are  prone  to 
think  of  a  consonance  as  something  which  sounds  well,  and  of  a  dis- 
sonance as  being  harsh  and  discordant;  but  in  a  harmonic  sense  the  im- 
port of  the  terms  is  far  wider.  A  consonance  is  a  combination  of  two  tones 
that  in  itself  produces  a  more  or  less  satisfactory  effect,  i.e.  is  complete, 
independent,  and  does  not  arouse  in  the  hearer  the  feeling  that  some  other 
combination  must  follow.  For  example,  if  any  one  of  the  following  inter  • 
vals  is  played  (of  course  with  pauses  between),  it  will  be  evident  that  each 
is  satisfactory  and  can  stand  by  itself  (i.e.  it  need  not  be  approached  in  any 
particular  way,  and  arouses  no  expectations  of  a  subsequent  interval). 


Henceforth  the  following  intervals  are  to  be  classified  and  considered  as 
consonances :  —  Perfect  Octaves,  Perfect  Unisons,  Perfect  Fourths,  and  Per- 
fect Fifths,  and  also  Major  and  Minor  Thirds  and  Sixths.  Upon  analysis 
it  will  be  seen  that  each  of  the  above  intervals  is  one  of  the  consonances 
enumerated.  In  like  manner  chords  composed  onhy  of  consonant  inter- 
vals are  independent,  satisfactory  in  themselves,  i.e.  they  may  both  begin 
and  end  a  sentence,  giving  an  effect  of  stability,  or  even,  if  used  too  much, 
of  inertia.  This  will  be  felt,  if  each  of  the  following  chords  is  played,  of 
course  with  appropriate  pauses. 


E|^EteEE=B 

I— *—\ 


16.  A  Dissonance,  on  the  other  hand,  is  a  combination  of  two  tones, 
which  in  itself  produces  an  impression  of  incompleteness;  it  is  unsatisfactory, 
dependent,  so  that  the  hearer  urgently  feels  that  something  must  follow 
before  a  logical  pause  can  be  made.  Play  on  the  pianoforte  each  one  of 
the  following  intervals,  pausing,  as  before,  after  each. 


Each  of  these  intervals  is  unsatisfactory  by  itself,  and  depends,  for  a  com- 
plete effect,  upon  something  else  to  follow.     We  now  place  after  each  of 


8  HARMONY 

these  dissonances  a  consonance,  and  the  combination  of  a  dissonance  followed 
by  a  consonance  is  felt  to  be  entirely  satisfactory. 


m 


'.  * 


:?.*>  ^  I  l-fr^r  -gz. 


123466  78 

The  dissonances  then  are  ofl  forms  of  2ds,  7ths,  and  9ths  and  all  augmented 
and  diminished  intervals;  in  like  manner,  a  dissonant  chord  is  one  which 
contains  at  least  ONE  dissonance  (not  necessarily  very  harsh),  and,  taken 
by  itself,  has  an  incomplete  effect.  Play  each  one  of  the  following  dissonant 
chords,  and  the  impression  of  incompleteness,  or  suspense,  is  plainly  felt. ! 

7  8 


/    Jr                    II 

1     90        1 

1          .,        |     a  ,        I 

I  ^ 

_o        1                  1     *^i 

1    11*     1    S'5' 

^ 

IftS         T                     - 

e»                f,,        \    Jt'2 

"tt^                  ^x- 

o 

Ik  1          01                       1 

\        &        \  W5> 

|      Vf9          \          &         \ 

rl 

JO,              ^L 

c\\  —  —  —  1—  fc  —    1— 

—&  1       o  1  

>5  1  —  H>5  1— 

-«  II 

J*  ** 

_fi£_       —  <»- 

—  a.  —  1—Q&— 

—  11 

1 

x= 

1               I 

II 

We  now  follow  each  of  these  dissonant  chords  with  a  consonant  chord,  and 
the  feeling  of  rest  and  satisfaction  is  evident  at  once. 


L   - 


gg^^l^^^l^g^g^  3^\ 


16.  The  consonance  following  the  dissonance  is  called  the  Chord 
of  Resolution  (the  laws  by  which  dissonances  are  appropriately  resolved 
are  fully  explained  later).  Consonance  is  a  point  of  rest,  and  dissonance  of 
unrest.  All  music,  in  a  broad  sense,  consists  of  a  happy  combination  of 
these  two  complementary  elements;  too  much  of  either  is  fatal,  for  exces- 
sive consonance  produces  stagnation,  while  too  many  dissonances  often 
result  in  irritation  and  undue  restlessness.  Dissonances  in  music  furnish 

l  The  student  should  analyze  and  name  each  one  of  the  dissonant  intervals  found  therein. 


HARMONY 


an  element  of  motion,  of  progress,  and  keep  the  mind  and  imagination  of 
the  hearer  aroused.  In  certain  of  the  above  resolutions  the  feeling  of 
rest  and  satisfaction  is  stronger  than  in  others,  and  oftentimes  more  than  a 
single  chord  is  needed  to  resolve  a  dissonance  satisfactorily.  A  dissonance, 
also,  does  not  always  resolve  at  once,  one  often  proceeding  to  another,  in 
order  that  the  feeling  of  suspense  and  of  striving  may  be  prolonged. 

17.  An  interval  is  said  to  be  inverted  when  the  relative  position  of  the 
two  notes  is  changed,  either  by  placing  the  lower  note  an  octave  higher 
or  the  upper  one  an  octave  lower. 


Thus  F-C   is  a  perfect  5th:    if  F  be  placed  above  C,  or  C  below  F,  in 
either  case  the  result  is  a  perfect  4th. 

Every  Unison  (1)  on  inversion  becomes  an   Octave  (8). 


2d  ' 
3d  " 
4th  " 
5th  " 
6th  " 
7th  " 
Octave  (8)  " 


7th. 
6th. 
5th. 
4th. 
3d. 
2d. 
Unison  (1). 


Major        intervals  on  inversion  become  Minor. 

Minor  "  "       Major. 

Augmented     "         "  "       Diminished. 

Diminished     "         "         "  "       Augmented. 

But  Perfect  Intervals  always  remain  Perfect ;  it  is  thus  seen,  as  said  before, 
that  the  perfect  intervals  (unisons,  4ths,  oths,  and  8ves)  differ  from  all 
others  in  not  changing  their  specific  kind  on  inversion. 

18.   The  student  should  now  verify  the  above  statements  by  a  careful 
analysis  of  the  following  table. 


10  HARMONY 


r»         •  •        • 

II  II 

19.   The  following  exercises  are  to  be  worked  out :  — 

(1)  Write  the  names  of  the  following  intervals;  indicate  those  that  are  consonant  by  (O, 
those  that  are  dissonant  by  (£>). 


~'xe? 


A  good  method  of  procedure  is  the  following:  —  Invariably  find  the  general  name  of  the 
interval  first  (i.e.  whether  it  is  a  3d,  5th,  6th,  etc.)  by  counting  the  number  of  degrees,  in- 
clusively; e.g.  (a)  above  is  some  kind  of  a  fifth,  for  D-A  includes  five  scale-degrees,  (e)  is  a 
second,  (*)  is  a  third,  etc.  When  possible  consider  the  lower  note  of  the  interval  as  the  key- 
note of  a  major  scale,  and  remember  that  the  successive  degrees  of  the  major  scale  form,  with 
the  key-note  of  the  same,  either  perfect  or  major  intervals;  i.e.  the  1st,  4th,  5th,  and  8ve 
are  perfect,  and  the  2d,  3d,  6th  and  7th,  are  major.  Then  observe  how  these  numerical 
intervals  are  altered  (made  larger  or  smaller)  by  the  use  of  accidentals.  When  the  lower 
note  is  not  the  key-note  of  any  ordinary  scale,  it  is  well  to  consider  what  the  interval  would 
be,  if  free  from  accidentals;  e.g.,  D-A  is  a  perfect  fifth;  if  the  lower  note  is  raised,  the  in- 
terval is  lessened  by  a  semitone  and  therefore  is  a  diminished  fifth. 

(2)  Write  (and  afterwards  play)  the  following  intervals:  a  minor  second  of  E,  of  Bb  and 
of  F;  a  diminished  third  of  CJ,  E,  and  Bb;  an  augmented  fourth  of  Ff,  Db,  and  CJ;  an  aug- 
mented 6th  of  Fb,  of  A,  and  of  Bb;  a  diminished  seventh  of  Ef,  FX,  and  C. 

20.  Considerable  attention  has  been  paid  to  .this  subject  of  inter- 
vals, and  the  above  exercises  should  be  worked  out  faithfully  and  patiently. 
Although  the  mistake  is  sometimes  made  of  considering  this  work  formal 
and  dry,  it  must  be  undertaken  and  conquered.  A  quick,  clear  insight 
into  the  nature  of  intervals  is  as  necessary  for  the  subsequent  study  of  har- 
mony, as  is  the  multiplication  table  for  the  study  of  mathematics.  Let 
systematic  attention  be  paid  to  quickness  and  accuracy  of  ear,  and  grad- 
ually the  two-fold  power  will  be  gained  of  hearing  with  the  eye  and  seeing 
with  the  ear;  i.e.  when  any  interval  is  seen,  the  musician  should  hear  it 
(to  himself)  and  be  able  to  sing  it,  and  conversely  when  an  interval  is  heard, 
it  should  be  possible  to  visualize  it  and  to  write  it  down  in  correct  notation. 
The  student '  is  not  expected  to  recognize  at  once  all  the  more  compli- 
cated intervals,  but  from  the  outset  a  definite  attempt  should  be  made  to 
realize  in  sound  major  and  minor  3ds,  the  perfect  and  the  diminished  5th, 
the  perfect  and  the  augmented  4th,  and  the  three  7ths,  major,  minor,  and 
diminished. 

1  The  teacher  can  likewise  add  considerable  interest  to  this  work,  by  selecting  certain 
well-known  melodies  illustrating  the  various  intervals.  For  instance,  the  beginning  of 
Wagner's  "Flying  Dutchman"  Overture  shows  a  striking  use  of  the  perfect  5th;  the  main 
theme  of  Beethoven's  3d  "Leonore"  Overture  contains  several  augmented  4ths,  etc. 


c 

HARMONY  11 


CHAPTER  II 

THE   SCALES 

21.  BEFORE  we  treat  of  chords  and  their  combinations,  something 
must  be  learned  of  the  evolution  l  and  formation  of  our  modern  scales, 
major,  minor,  and  chromatic.  The  scale  gets  its  name  from  an  analogy  to 
the  steps  of  a  ladder  (Latin  scala).  All  nations  that  have  made  music 
have  agreed  in  adopting  some  selection  of  tones  as  a  scale,  although  the 
same  series  has  not  by  any  means  been  used  by  all.  Any  succession  of 
tones  may  be  said  to  form  a  scale,  and  these  tones  may  be  smoothly  con- 
nected (diatonically),  or  skips  may  appear  between  certain  of  them.  Dur- 
ing the  history  of  music  there  have  actually  been  in  use  scales  of  three, 
four,  five,  six,  seven  tones  and  more.  All  musical  peoples,  however,  ap- 
pear to  have  appreciated  the  intimate  natural  relationship  between  tones 
lying  that  distance  apart  which  we  call  an  octave',  the  differences  are  in  the 
intermediate  steps.  In  modern  music  we  employ  a  series  of  seven  steps, 
called  the  diatonic  scale,  with  the  power  of  interposing  certain  intermediate 
chromatic  steps.  The  major  diatonic  scale,  then,  is  as  follows: 


(For  the  definition  see  Chapter  I,  7.)      The  pattern  of  the  major  scale 
fixed,  and  there  is  but  one  form,  the  same  for  all  major  keys. 
22.    The  formation  of  the  minor  diato:iic  scale  is  as  follows: 


Min.  3d. 


II 


The  first  and  most  important  characteristic  of  the  minor  scale  is  the  minor 
third  between  the  key-note  and  the  third  degree.  The  half-steps  are  be- 
tween the  2d  and  3d,  5th  and  (5th,  and  7th  and  Stli  degrees,  while  between 
the  6th  and  7th  degrees  is  the  striking  interval  of  a  step  and  a  half  —  an 

1  Historically  considered  the  growth  of  modern  scales  and  of  chords  went  on  at  the 
same  time,  each  reacting  upon  the  other;  but  from  our  present  point  of  view  we  shall  explain 
chords  as  being  founded  upon  the  successive  degrees  of  accepted  scale  systems.  Those  who 
deiire  more  knowledge  on  this  very  important  and  interesting  subject  are  advised  to  read 
the  second  chapter  of  Parry's  "Involution  of  the  Art  of  Music,"  and  also  the  article  on  the 
fireek  Modes  in  Orove's  "  Dictionary  of  Music." 


12 


HARMONY 


augmented  2cl.  The  minor  scale  in  distinction  from  the  major  has 
an  elastic  scheme,  and  appears  in  three  forms  ascending  and  three  descend- 
ing, as  follows: 

(a)  (b)  (c) 


7     s--—^ 

-.-ll--^ 

r~»-*~*~l 

*r—  *-*-^- 

Q-      ^g~—  ff*  •  B  r^—  It*  &•  a  r^  •—  •—  .                         r. 

-^                                               •       •       ^        — 

:  —  •—»  — 

'•*«• 

-18^  -                               • 

j 

•  c 

(a),  (6),  (<f)  and  (/)  are  the  forms  chiefly  used  in  chord  formation;  (c)  and  (/)  are  much  used 
melodically,  but  are  obviously  not  characteristic,  being  only  the  relative  major  scale  begun 
on  a  different  tone;  (6)  is  also  much  used  melodically,  but  (e)  is  seldom  found  in  modern  music, 
although  it  was  often  employed  by  Bach  and  his  contemporaries. ' 

The  minor  scale,  it  will  be  observed,  always  begins  with  a  minor  third. 

23.  Theoretic-ally,  scales  may  begin  upon  any  tone  chosen,  and 
conformation  made  to  the  above  patterns  by  the  introduction  of  appro- 
priate  accidentals;  i.e.  there  may  be  major  and  minor  scales  on  C,  C$,  D, 
D$,  E,  E$,  etc.  Practically  only  a  certain  number  of  theso  scales  is  in  com- 
mon use,  for  some  of  them  would  contain  so  many  accidentals  as  to  make 
the  reading  of  the  notes  difficult.2  As  to  the  formation  of  scales  in  prac- 
tical use,  experiment  showed  that  if  a  scale  were  begun  on  the  fifth  degree 
of  the  above  scale  of  C  major,  the  same  series  of  notes  could  be  used  ana 
the  same  combination  of  tones  and  semitones  would  result  with  one  excep- 
tion, e.g- 


U  major. 

1          2 

3          4 

6 

0      ..  7         8 

-   ^     i     <5 

^  

^5     S?    i   lff-" 

3fe                   ^    l~75?  —  *  —  ^  : 

-—  

C  major. 


The  F,  the  seventh  degree,  or  leading-tone,  as  we  shall  call  it  later,  has  to 
be  raised  a  semitone  to  preserve  the  same  relativity  of  tones  and  semi- 

1  In  Bach's  "Chromatic  Fantasie"  will  be  found  striking  instances  of  the    manner 
in  which  different  forms  of  the  same  minor  scale  are  used  in  the  same  passage. 

2  In  complicated  chromatic  modulations,  however,  we  sometimes  find,  for  a  few  meas- 
ures, chords  written  in  very  extreme  keys.     For  instance,  near  the  beginning  of  Liszt's  song 
to  Goethe's  "'lignon,"  there  is  a  passage  in  the  key  of  AJ  major.     No  one,  however,  wouH 
begin  a  composition   in   AJ  major,  for  the  enharmonic  Bb  (A3=Bl7)  with   two   flats  in   the 
signature  is  far  easier  to  read  than   AJ,  the  key  of  ten  sharps.      Compare    also  the  opening 
measures  of  Schumann's  "Carnaval"   for  chords  written   in  the   key  of  Fb   major  (8  flats) 
instead  of  the  enharmonic  £  major  (4  sharps). 


HARMONY 


13 


tones  as  in  the  scale  of  C  major.  The  other  sharp  keys  are  formed  in  like 
manner.  The  formula  may  be  stated  as  follows :  —  to  construct  major 
scales  by  the  introduction  of  sharps,  begin  in  each  case  with  the  fifth  degree 
of  the  old  scale  and  raise  the  seventh  degree  of  the  new  scale  a  semitone, 
continuing  till  every  one  of  the  seven  different  tones  has  been  sharped,  e.g. 


V,     J>3>   A  ^ 

t(\\                                                                                                          0                   U        i    i"         <"2 

L-*-     T, 

C?     tf^ 

5              x"^.     L 

etc. 

H^  —  ^  1. 

In  actual  music  it  is  not  customary  to  write  the  sharps  or  flats  in  connec- 
tion with  each  note;  they  are  grouped  together  at  the  beginning  of  the 
piece  and  form  what  is  known  as  the  signature,  being  placed  in  order  from 
left  to  right  on  the  scale-degrees  influenced  in  any  given  case.  The  signa- 
tures of  the  different  sharp  keys  are  as  follows: 

G  D  A  E  B  Fj 


24.  If  this  series  be  continued,  the  next  key-notes  in  order  will  be  G$, 
D$,  AjJ,  E$,  and  B$.  But  as  all  these  keys  involve  the  use  of  double  sharps 
—  the  signature  of  B$  major,  for  instance,  would  be 


—  in  practically  every  case  it  is  more  convenient  to  use  the  enharmonic-flat 
scale.  With  B$  major,  the  enharmonic  of  C  major,  the  series  closes;  for 
we  have  now  completed  the  "circle  of  fifths,"  as  it  is  termed,  going  through 
the  sharp  keys  with  ascending  perfect  fifths.  The  circle  may  be  represented 
as  follows: 

Read  around  to  the  right. 


14 


HARMONY 


26.  The  flat  scales  are  formed  in  succession  by  an  analogous  proceed- 
ing; i.e.  starting  with  C  major,  if  a  new  scale  is  begun  in  every  case  on  the 
degree  a  perfect  fifth  below,  the  normal  order  of  tones  and  semitones  is  pre- 
served with  the  need  of  but  one  change,  e.g. 


etc. 


That  is,  in  the  major  scale  starting  on  F,  the  fourth  degree  has  to  be  low- 
ered a  semitone,  that  the  series  may  conform  to  the  established  pattern. 
The  other  flat  scales  are  formed  in  like  manner;  i.e.  the  key-notes  descend 
by  perfect  fifths,  and  in  every  case  the  fourth  degree  of  the  new  scale  is  to 
be  lowered.  The  signatures  of  the  different  flat  keys  are  as  follows : 


As  in  the  case  of  sharp  keys,  the  series  might  be  continued,  but  as  soon  as 
double  flats  would  be  necessary  the  enharmonic-sharp  key  is  preferred. 


Read  around  to  the  left. 
C 


A« 


26.   As  keys  which  have  more  than  six  sharps  or  six  flats  are  s-    :ewhat 
complicated  in  notation  it  is  customary  to  use  the  simpler  enharmonic,  i.e. 


HARMONY  15 

B  (5  sharps)  instead  of  d?  (7  flats)  and  likewise  Dt>  (5  flats)  instead  of  C$ 
(7  sharps).    This  will  be  made  clear  by  the  following  circle  of  keys: 


It  is  therefore  evident  that  twelve  major  scales  are  commonly  employed, 
and  as  we  shall  soon  see  that  every  major  scale  has  its  relative  minor,  twenty- 
four  l  major  and  minor  scales  are  commonly  held  to  be  the  basis  of  our 
harmonic  system. 

27.  The  minor  scale  is  composed  of  the  same  tones  (with  one  excep- 
tion) as  is  the  corresponding  major  scale  to  which  it  is  said  to  be  related, 
and  its  tonic  is  a  minor  third  below  that  of  the  latter;  the  one  tone  differ- 
ent in  the  two  scales  is  so  because  of  the  fact  that  the  so-called  leading- 
tone  in  every  major  and  minor  scale  is  a  semitone  below  the  tonic.  The 
evident  relationship  of  these  major  and  minor  scales,  and  the  single  dif- 
ference that  exists  between  them  are  shown  thus. 


y 

/L 

[   |(TV 

— 

- 

[  V  \J 

m         9         m 

e 


(If  the  seventh  degree  (leading-tone)  be  not  raised  chromatically,  one  of 
the  most  characteristic  features  of  the  scale  is  lost.) 

The   above   scale,   with   an   augmented    second  between   the  6th  and  7th 
degrees,  is  called  the  harmonic  minor   scale,  in  distinction  from  various 

1  It  may  serve  as  an  aid  to  memory  to  recall  the  fact  that  J.  S.  Bach'*  work,  the  "  Well- 
Tempered  Clavichord,"  is  often  referred  to  an  the  "48  Preludes  and  I'ujtues":  thnt  is,  two 
preludes  and  two  fugue*  were  composed  for  each  of  the  •-<•!  of  twelve  major  and  twelve  minor 
keys.  In  Beethoven's  " /wei  Priiludien  durrh  alle  Dur-Tonarten,"  op.  39,  will  be  found  an 
example  of  modulation  through  all  the  major  keys. 


16 


HARMONY 


forms  chiefly  used  for  melodic  purposes  (see  Chapter  II,  22).  Many 
important  and  necessary  facts  will  be  learned  when  we  come  to  speak  of 
the  chords  formed  on  the  degrees  of  the  minor  scale  and  begin  to  write 
exercises  in  that  mode.  At  present  we  have  only  touched  upon  the  main 
points  with  reference  to  scale-formation. 

28.  The  chromatic  scale,  so  important  in  modern  music,  melodically 
and  also  harmonically,  is  composed  entirely  of  half-steps,  i.e.  it  includes 
the  twelve  semitones  to  be  found  within  the  octave.  The  grammatically 
correct  notation  of  the  chromatic  scale  of  C  would  be  as  follows: 


a  different  notation,  however,  is  often  used,  being  somewhat  easier  to  read 
on  account  of  the  fewer  accidentals. 


:|^L|^^_ 
~* in 


In  writing  the  chromatic  scale,  composers  have  been  uncertain  and  careless 
in  the  employment  of  the  necessary  accidentals;  in  Beethoven's  pianoforte 
concerto  in  G  major,  for  example,  the  chromatic  scale  being  written  in 
four  different  ways. 

It  might  be  argued  that  sharps  should  be  employed  in  an  ascending  scale,  and  flats 
in  a  descending  one;  but,  on  the  other  hand,  the  following  examples  would  look  absurd  and 
be  illogical  as  written. 


The  best  notation  of  the  chromatic  scale  in  any  given  case  is  a  point  as 
to  which  no  specific  directions  can  be  given ;  common  sense  and  experience 
must  decide. 

29.  In  preparation  for  the  formation  of  chords,  it  is  necessary  to  become 
familiar  with  the  technical  names  of  the  various  scale-degrees  in  distinc- 
tion from  the  mere  numerical  designation  of  2d,  3d,  etc.,  especially  as 


HARMONY 


17 


the  derivation  of  these  terms  conveys  much  meaning.  The  first  tone 
popularly  known  as  the  key-note,  is  called  the  Tonic:  this  is  an  abbre- 
viation of  the  Latin  Tonica,  and  means  the  Tone,  i.e.,  the  chief  tone  with 
which  the  scale  begins,  and  to  which  each  one  of  the  other  tones  (both 
diatonic  and  chromatic)  bears  a  definite  relationship.  A  similar  term  is 
Tonality,  the  full  import  of  which  will  be  understood  when  we  come 
to  learn  about  the  principal  chords  in  a  key.  The  most  important  tone 
after  the  tonic  is  the  fifth,  called  the  Dominant,  on  account  of  its  ruling 
influence  upon  the  key.  The  fourth  tone  of  the  scale  is  called  the  Sub- 
Dominant  or  lower  dominant,  because  it  lies  the  same  distance  below  the 
tonic  that  the  dominant  lies  above  it.  On  this  point  the  student  should 
be  perfectly  clear  from  the  outset;  every  tonic  has  two  dominants,  one  a 
perfect  fifth  above,  called  the  dominant,  the  other  a  perfect  fifth  below,  called 
the  sub-  or  under-dominant.  The  chart  makes  this  clear. 

Tonic.  Dominant. 


I] 


Sub-Dom- 
inant. 

The  sub-dominant  is  never  to  be  explained  as  being  so  called  because  it 
is  the  tone  below  the  dominant.  The  third  tone  is  called  the  Mediant,  as 
it  is  midway  between  the  tonic  and  the  dominant.  In  like  manner  the 
sixth  tone  is  called  the  Sub-Mediant,  or  lower  mediant,  as  it  is  midway  be- 
tween the  sub-dominant  and  tonic. 

Tonic.     Dominant. 


Sub-Mediant. 


-- £- 


Bab-Dom- 
inant. 

The  second  tone  of  the  wale  is  called  the  Super-Tonic,  i.e.  the  one  above 
the  tonic.  The  seventh  tone,  on  account  of  its  tendency  to  ri.-w  or  lend  up 
to  the  tonic,  is  called  the  Lcailing-Tone.*  This  is  the  most  important  of  a 
class  called  Tendency  Tones,  and  great  care  is  always  to  be  exercised  in  its 
treatment. 

1  The  French  term  for  this  seventh  degree  of  the  wale  is  "la  note  sensible."  i.e.  the 
sensitive  note. 


18 


11AUMONY 


CHAPTER  III 

/  -* 

/  TRIADS 

30.  HAVING  now  defined  intervals  and  their  inversions,  and  stated 
the  main  facts  in  regard  to  scales,  we  come  to  the  construction  of  chords, 
and  the  manner  of  their  connection.  A  chord,  in  its  uninverted  form,  is? 
a  combination  of  three  or  more  tones,  each  of  them  being  either  a  major 
or  minor  third  above  the  tone  below  it.  Combinations  of  three  different' 
tones  are  called  Triads,  and  consist  of  a  low  tone  and  the  third  and  fifth 
above.  Chords  of  four  different  tones  are  called  Seventh  chords,  and  are 
merely  triads  with  an  additional  tone,  i.e.  1,  3,  5,  7.1  The  most  con- 
venient name  for  the  tone  on  which  any  uninverted  chord  is  founded  is 
the  ROOT,  a  term  always  to  be  understood  as  having  that  meaning,  the 
lowest  tone  of  other  (inverted)  chords  being  called  the  bass.  Triads  appear 
in  many  forms  in  accordance  with  the  specific  varieties  of  the  thirds  and 
fifths;  for  example  the  following  chords  are  all  triads. 


(a) 


(6) 


31.  A  triad  with  a  perfect  fifth  and  a  major  third  is  called  a  MAJOJB 
TRIAD  (Ex.  o) ;  with  a  perfect  fifth  and  a  minor  third,  a  MINOR  TRIAD  (Ex.  6>. 
All  other  triads,  DIMINISHED  (Ex.  c,  e),  AUGMENTED  (Ex.  d),  are  dissonant  in 
their  nature  and1  require  careful  treatment.     Our  first  exercises  will  con- 
sist largely  of  major  and  minor  triads. 

32.  On  each  of  the  seven  tones  in  every  major  and  minor  scale  there 
can  be  erected  a. triad.      Those  on  the  degrees  of  the  major  scale  are  as 
follows:  *^v- 


y:_ 

*2     '  '  X          !y 

-4k—  «- 

g 

X 

-£= 

=t    ^  •    »  t 

in      IV 


VI         VI1° 


Of  this  series  the  tonic,  dominant    and   sub-dominant  triads  are  major 
(hence  marked  with  a  large  Roman  numeral).     The  triads  on  the  second, 

1  The  aeries  may  be  continued  by  thirds  to  chords  of  the  ninth,  and  even  in  some  cases 
to  chords  of  the  eleventh  and  thirteenth,  e.g. 


HARMONY 


19 


third,  and  sixth  degrees  are  minor  (small  numerals),  and  that  on  the  lead- 
ing-tone diminished  (vn°).  (This  last  triad  will  be  sparingly  used  until  we 
come  to  inverted  chords.)  The  triads  on  I,  V,  and  IV,  are  the  most  impor- 
tant, as  they  have  a  close  connection  with  each  other,  and  when  used  in 
combination  always  define  clearly  the  tonality. 

33.  Triads,  and  in  fact  ah1  chords,  have  a  natural  connection  when 
they  have  a  tone  or  more  in  common;  the  following  chart  shows  the  rela- 
tionship of  the  three  principal  triads. 


Dominant 

Sub-Domi- 

Tonic 

Triad. 

S3 

n 

nant  Triad. 

Triad. 

& 

J 

i  

fT 

S3 

<5 

fm 

f^ 

j 

\  J 

0   \  

IV  I  V 

Triads  with  two  tones  in  common  have  a  particularly  close  relationship; 
this  happens  when  their  roots  are  a  third  apart.  Triads  on  adjoining  de- 
grees of  the  scale  have  obviously  no  common  tone. 

34.  Our  first  exercises  are  to  be  simple  combinations  of  chords  for 
four  voices,  soprano,  alto,  tenor,  bass.1  The  usual  compass  of  the  voices 
may  be  set  as  follows,  although  for  solo  singers  these  limits  are  frequently 
exceeded. 


Soprano. 


Tenor. 


II 


Alto. 


Bass. 


II 


36.  As  there  are  but  three  tones  in  triads,  and  we  have  four  voices, 
it  is  necessary  that  in  every  chord  one  of  the  tones  shall  be  doubled,  being 
sung  by  two  voices.  .As  a  general  thing,  the  mos£  satisfactory  result  is  obtained 

1  For  the  present  the  normal  relative  position  of  these  four  voices  is  to  be  preserved, 
and  they  are  not  allowed  to  cross  each  other  (soprano  below  alto,  alto  below  tenor,  bass  above 
tenor)  e.g. 


The  musical  effect  result  inn  from  the  crossing  of  voices  can  be  very  (food,  but  will  not 
be  so  unless  planned  by  a  writer  of  experience  and  taste;  the  student  must  absolutely 
avoid  it. 


20 


HARMONY 


by  doubling  the  root;  the  third  is  doubled  when  the  leading  of  the  voices  brings 
that  result  about  naturally  and  logically;  the  chord  is  less  strong  when  the  fifth 
is  doubled  ',  bad  voice-leading  often  also  resulting. 

36.  When  the  three  upper  voices  (soprano,  alto  and  tenor)  lie 
within  less  than  an  octave,  the  harmony  is  said  to  be  in  close  position, 
whether  the  bass  be  near  the  tenor  or  far  removed ;  if  the  three  upper 
voices  are  more  evenly  distributed,  covering  more  than  an  octave,  we  have 
open  position ;  when  they  cover  exactly  an  octave,  we  may  consider  that 
we  have  either  close  or  open  position,  being  determined  as  to  this  point  by 
the  chords  preceding  or  following.  Wherever  there  is  to  be  a  wide  interval 
between  any  of  the  voices  it  should  be  almost  always  between  bass  and 
tenor,  and,  excepting  for  an  occasional  chord,  there  should  never  be  a  larger 
interval  than  an  octave  between  soprano  and  alto,  or  alto  and  tenor. 


Close  Position. 
fnffitt       gJ     -  J       I  >? 


Open  Position. 


-&1       A.        -&L 


r=r 


r 


II 


Whether  in  any  particular  case  open  or  close  position  shall  be  employed 
will  depend  on  the  leading  of  the  voices,  sometimes  on  the  mere  sound  of 
the  chord,  often  again  on  practicability  (for  there  are  successions  of  chords 
that  can  be  written  effectively  in  but  one  kind  of  position).  The  student 
is  strongly  advised  to  use  both  positions  from  the  first,  for  only  in  this  way 
can  ease  and  pliability  in  part-writing  be  obtained.  In  many  cases  it  is 
well  to  try  both  ways,  and  to  cultivate  the  judgment  by  selecting  the  one 
preferable. 


>  As  to  doubling  of  the  M,  cf.  pp.  29, 3^,41, 50.  Doubling  of  the  5th  sometimes  results 
In  such  a  disposition  of  the  voices  as  to  render  g^od  voice-leading  i  npossible.  In  the  fol- 
lowing, eg.  the  tenor  produces  consecutive  fcves  by  descending  to  F,  and  consecutive  5ths 
If  it  ascends  to  A ;  it  is  obvious  that  we  must  change  the  first  chord  and  double  its  root. 


HARMONY  21 

With  triads  it  is  obvious  that  in  every  chord  the  root  must  be  present,  as 
that  is  the  tone  on  which  it  is  based.  Without  this  we  shall  not  know 
with  what  triad  we  have  to  do;  the  third  must  also  be  heard,  as  de- 
termining whether  the  triad  be  major  or  minor.  In  some  cases  it  is  not 
absolutely  necessary  to  have  the  fifth,  when  the  leading  of  the  voices  causes 
it  to  be  naturally  omitted,  without  our  being  doubtful  whether  the  chord 


be  a  triad  or  not. 


3d  omitted  ( bad. )         5th  omitted  (  good.) 


II 


J 


II 


37.  Here  follow  examples  of  different  groupings  of  the  triad  C-E-G, 
to  illustrate  principles  of  doubling  and  spacing',  each  chord  should  be  care- 
fully played  and  the  effect  analyzed.  It  is  to  be  understood  that  the  rela- 
tive position  of  the  upper  notes  of  a  chord  makes  no  difference  in  its  nature, 
provided  the  bass  be  unchanged.  In  the  following  chords,  C,  E,  G  are  the 
only  different  notes  used,  and  in  each,  C,  the  root  of  the  triad,  is  in  the  bass. 
In  fact  all  chords  in  which  the  root  is  the  lowest  tone  are  said  to  be  in 
"root  (or  fundamental)  position"  in  distinction  from  inverted  positions,  of 
which  we  shall  learn  later. 


^||llilii|=  i|j| 


38.  In  combining  chords  the  two  most  important  principles  arc  these: 
1st,  the  melodic  progression  of  each  single  voice,  and  2d,  the  harmonic  pro- 
gression of  each  part  in  its  relationship  to  the  others.  A  good  melody  is 
one  that  proceeds  naturally  and  without  awkward  skips;  hence  melodies 
in  general  should  be  diatonic  in  character,  although  simple  skips  of  .'ids, 
4ths,  ")ths,  and  Gths,  may  be  introduced  for  variety.  In  our  early  work  no 
skips  of  a  7th  or  of  any  augmented  or  diminished  interval  are  to  be  used: 


22 


HARMONY 


the  only  exception  to  this  being  the  diminished  5th,  which  may  be  intro- 
duced when  one  of  the  tones  is  the  leading-tone ;  e.g. 


q 


39.   As  regards  harmonic  progression,  there  are  three  kinds  of  part- 
motion.    Similar  motion  occurs  when  voices  move  in  the  same  direction ;  e.g. 


"- 


in  contrary  motion  they  move  in  opposite  directions  (i.e.  one  part  ascends, 
while  the  other  descends) , 


and  in  oblique  motion  one  voice  stays  on  the  same  tone,  while  the  other 
moves  up  or  down. 


J5^     -Jl-j       |£y=d=n 

pEpp    3=^==^=       II 
wr    ui     L^  r 


40.  It  is  evident  that  in  four-part  harmony  ordinarily  at  least  two ' 
of  these  different  kinds  of  motion  must  be  combined. 

*  This  does  not  apply  where  successive  chords  are  mere  changes  in  position; 


we  shall  also  meet  later  with  chord  successions  in  which  similar  motion  of  all  fmtr  voices  is  of 
perfectly  good  effect,  and  often  preferable  or  even  necessary; 


»— 

r—r*      • —    •  —  *  _  L*^-.*"---*1 


but  it  mutt  seldom  be  used  in  connecting  different  triads  in  root  position.  When  notes  are  t  led 
(the  tones  prolonged  in  the  same  voices  into  the  next  chord),  the  other  voices  man,  &  if  true, 
proceed  in  similar  motion,  though  never  in  such  a  way  as  to  produce  consecutive  8ves  or  5ths. 


HARMONY 


23 


Triads  whose  roots  are  separated  by  a  3d,  a  4th,  a  5th,  or  a  6th,  always 
have  tones  in  common  and  may  be  naturally  connected  by  a  combination 
of  oblique  and  similar  motion.  The  common  tones  should  largely  be  placed  in 
the  inner  voices,  in  order  that  the  soprano  may  have  melodic  movement 
and  variety,  e.g. 


V 

1 

1' 

\ 

! 

jf            ZZI2S  Ha 

1 

J 

!         1 

E  •  —  a 

H/l\                          —  —                         iS 

1 

eg  -*"^  ^ 

A 

—  •—  82         1 

VM  /                         ^^                    J*^ 

I 

z 

.y                  1 

.^-i              .*^i 

j'      p  —  i 

A-A 

-J^^L 

j 

p*s  rp 

I          I 

r\- 

-^ 

^x               ^^ 

T.         t 

5J_ 

r? 

^^     „     — 

& 

: 

&  • 

/*^ 

I 

\ 

IV 


41.   Triads  whose  roots  are  on  adjacent  degrees  of  the  scale  never  have 
common  tones,  e.g. 


Eisl, 


V      IV 


1         If 


In  connecting  such  triads  we  find  that  at  least  two,  often  all,  of  the  upper 
voices  are  to  be  led  in  contrary  motion  to  the  bass,  e.g. 


Never. 


Good. 


CONSECUTIVE  OCTAVES    AND    FIFTHS 


42.    The  first,  and  most  important,  absolute  prohibition  which  wo  moot 
in   composition   is  this:    consecutive  Sirs,   unisons,  and  5ths  arc  forbidden. 


24 


HARMONY 


That  is:  no  two  parts  may  more  in  perfect  8ves,  unisons,  or  5ths,  with  one 
another,1  (c/.  p.  106). 


Voices  are  considered  to  be  an  8ve  or  5th  apart,  even  when  separated   by  more  than 
one  octave: 


There  is  good  reason  for  this.  Taking  CONSECUTIVE  OCTAVES  first,  it  is 
admitted  that  they  do  not  sound  badly.  But  it  must  be  remembered  that  we 
are  dealing  with  four  independent  voices,  and  if  two  of  them  go  on  singing 
the  same  tones,  either  in  unison  or  an  octave  apart,  we  have  practically  re- 
duced the  number  of  different  voices,  as  we  hear  them,  to  three.  Moreover, 
the  voices  that  double  the  melody  stand  out  so  conspicuously  against  their 
weaker  companions  (the  latter  not  being  doubled)  that  the  proper  balance 
is  destroyed.  On  the  other  hand,  when  this  very  effect  of  a  preponderance 
of  one  part  is  desired  by  a  composer,  he  resorts  to  just  such  means;  for 
instance,  in  the  following  choral  from  Mendelssohn,  and  in  many  of  Beet- 
hoven's string-quartets. 


MENDELSSOHN;  Choral  from  "St.  Paul" 


1  It  may  be  asked  why  these  octaves  and  fifths  are  prohibited,  although  found  in  the 
works  of  many  great  composers.  The  answer  is  simple;  the  student  is  not  in  a  position  to 
allow  himself  liberties  that  are  only  permissible  to  those  who  have  experience  and  mature 
judgment. 


HARMONY  25 

BEETHOVEN;  Op.  59,  No.  1,  (Scherzo) 


etc. 


Octaves,  and  fifths  to  a  less  degree,  will  be  found  in  most  chords  in  four-part 
harmony;  these  8ves  and  oths  are  not  consecutive  unless  occurring  between 
the  same  two  MOVING  voices  in  succession,  e.g. 


\7~   rrr 


(The  student  is  to  assure  himself  that  this  passage  contains  no  consecutive  octaves.) 

43.  With  CONSECUTIVE  FIFTHS  the  matter  is  different:  they  often  do 
sound  badly.  The  fact  that  certain  composers  have  been  skilful  enough  to 
manage  them  so  that  in  particular  cases  they  are  satisfactory,  is  no  argu- 
ment that  the  inexperienced  student  may  make  experiments  in  that  direc- 
tion. He  will  probably  fail,  and  had  better  not  waste  his  time  in  trying. 

The  following  example  will  roughly  show  varying  degrees  of  badness  and  harmlessness 
as  regards  Sths. 


The  triads  (a)  sound  really  ugly,  largely  because  of  the  consecutive  major  thirds.  The  period 
(6)  is  not  so  harnh;  and  consecutive  fifths  are  by  no  means  infrequent  in  triads  (<•)  which  have 
tones  in  common.  This  is  especially  true  of  consecutive  fifths  between  the  tonic  and  domi- 
nant chords;  e.g. 

BKKTHOVKN  (Pastoral  Symphony) 

—4 


1 


^^STTT^E/          ^d 

— :arfp— ifd  ritf 

>.J  " 


etc. 


=*-r 

IV 


26  HARMONY 

Successions  like  the  following  are  often  met  with  in  instrumental  music. 


I          '  ! 

The  following  example    from   an   Etude  of  Chopin,   shows  what    a  beautiful  effect  of 
mere  sound  can  be  produced,  in  part  as  a  result  of  consecutive  fifths. 


In  our  early  exercises  the  opportunity  for  unsatisfactory  fifths  will  occur  when  triads  on  ad- 
joining degrees  are  to  be  connected,  as  in  this  ease  the  lack  of  a  common  tone  causes  a  feeling 
of  disjunction,  and  the  prohibition  of  consecutive  fifths  must  be  strictly  attended  to. 

Consecutive  8ves  and  Sthscan  occur  bet  ween  any  two  voices,  and  in  discussing  the  chord 
of  the  sixth,  which  follows  naturally  after  the  triad  (being  an  inversion  of  it)  we  shall  have  to 
pay  attention  especially  to  the  danger  of  such  progressions  occurring  between  soprano  and 
alto,  and  alto  and  tenor.  But  for  the  present  we  are  safe  in  confining  our  attention  to  con- 
secutive 8ves  and  Sths  between  the  bass  and  any  one  of  the  other  voices. 

44.  Before  going  on  to  other  principles  of  chord  connection,  it  will  be 
well  to  say  something  of  what  is  meant  by  the  term  "good  leading  of  the 
parts."  As  most  persons  are  acquainted  with  music  chiefly  as  presented 
to  them  through  the  medium  of  the  pianoforte,  it  is  often  a  new  idea  that 
the  different  tones  in  such  chords  really  belong  to  different  voices,  and 
that  these  voices,  even  in  instrumental  music  (and  always  in  vocal  music), 
should  have  individual  melodic  movement. 

This  principle  is  not  obvious  in  most  pianoforte  music,  disguised  as  it  is  by  the  fact 
that  other  tones  are  often  added  to  those  representing  the  real  voice  parts,  in  order  to  obtain 
greater  sonority,  or  a  better  quality  of  sound,  or  for  some  reason  connected  with  the  techni- 
cal side  of  pianoforte  writing. 

Ciiorrs*,  Nocturne  Op.  9,  No.  1 


HARMONY 

SCHUMANN,  "  Faschingsschwank,"  Op.  26 

-4-H 


1=3==          ^g:=  ^~ J^lEg  jz|?EgE 

*  "*— *  "          _«.      .«-  W         W      3* 


etc. 


In  the  first  illustration  from  Schumann,  the  number  of  note*  in  the  chords  varies 
for  pianistic  reasons;  in  the  second,  rests  have  been  added  (not  indicated  by  the  composer) 
to  define  more  clearly  the  voice-parts;  such  rests  are  generally  omitted  for  convenience  in 
writing  out  pianoforte  music. 

45.  In  orchestral  music  the  principle  that  voice-parts  shall  be  real  ones,  having  me- 
lodic value,  is  carried  out  so  far  as  conditions  permit,  although  necessary  latitude  is  allowed 
in  that  so-called  'filling  in"  voices  are  freely  used  when  desired.  A  pood  illustration  of  ad- 
herence to  strict  part-writing  will  be  found  in  the  first  movement  of  Beethoven's  C  minor 
symphony,  and  in  Bach  will  be  seen  an  almost  unvarying  employment  of  melodic  part-writing 
in  the  orchestra;  in  string  trios,  quartets,  etc.,  good  partAvriting  is  absolutely  demanded. 

It  is  well  to  say  all  this  at  first  to  confirm  the  student's  mind  in  the  idea  that  writ- 
ing in  real  parts  is  eminently  desirable  in  good  music. 

In  all  our  work  we  shall  consider  ourselves  as  dealing  with  real  voices, 
and  therefore  shall  obviously  have  for  a  prime  requisite  good  and  inde- 
pendent melodic  movement  of  each  voice.  If  a  choice  be  necessary,  and  there 
be  a  question  whether  the  soprano  or  an  inner  voice  (alto  or  tenor)  shall 
be  melodic,  it  is  ordinarily  the  soprano  that  should  have  the  preference;  and 
we  may  state  now  that  in  the  quartet  of  voices,  soprano  and  bass  are  usually 
of  most  importance. 


"  Harvard  Hymn' 
SOI-KANO 


JOHN  KNOWI.KS  PAIXK 


=3-  :"i" 

•    ,    •    •       •    , 


THNOR 


28 


HARMONY 


SOPRANO 


TENOR 

Compare  these:  soprano  and  bass,  without  the  other  voices,  do  not  produce  an  entirely 
satisfying  effect,  but  the  result  is  sense,  the  hearer  instinctively  supplying  what  is  felt  to  be 
missing.  Without  the  soprano  we  are  at  a  loss  to  know  what  is  the  melody;  if  we  are  not 
given  the  bass  (which  determines  the  harmonies  of  the  superstructure)  we  can  only  guess  at 
what  that  was  intended  to  be.  From  this  it  is  seen  that  soprano  and  bass  are  the  vital  parts 
of  all  chords,  excepting  that  when  the  chief  melody  happens  to  be  given  to  an  inner  part,  alto 
or  tenor,  the  soprano  becomes  of  secondary  importance.  (Write  out  the  above  illustration 
with  all  four  parts  complete,  and  play  it,  comparing  with  what  is  given  above.) 

46.  The  seventh  tone  of  the  scale,  always  a  semitone  below  the  tonic, 
is  of  especial  importance,  since  it  is  the  only  one  that  has  of  itself  a  distinct 
tendency  to  move  in  a  particular  direction.  With  our  modern  system  of  key 
tonality  it  has  become  an  instinct  for  us  to  demand  this  rising  of  the  7th 
to  the  tonic;  hence  the  name  of  leading-tone.  Moreover,  it  is  the  essential 
factor  in  modulation,  and,  indeed,  is  almost  always  needed  to  fix  a  modu- 
lation with  definiteness.  Being  a  tone  so  very  important  and  one 
naturally  catching  our  attention  quickly,  it  must  not  be  over-emphasized, 
for  it  belongs  to  the  class  of  so-called  "sensitive"  tones,1  and  therefore 
must  not  be  doubled  as  a  rule. 

This  accounts  for  the  infrequent  use  of  the  triad  on  the  7th  degree  (in 
the  fundamental  position),  for  its  root,  which  we  should  naturally  double,  is 
the  leading-tone.  N.B.  Avoid  the  term  seventh  in  speaking  of  the  leading- 
tone,  as  later,  when  we  have  to  do  with  CHORDS  of  the  seventh,  the  two  things 
easily  become  confused  in  one's  mind. 

This  tendency  of  the  leading-tone  to  ascend  is  particularly  strong  when  it  is  the  third  of  the 
dominant  triad  and  the  succeeding  chord  is  the  tonic  triad,  and 'is  also  more  binding  in  con- 
nection with  the  soprano  than  with  the  inner  voices,  e.g. 


V  1  V 

When  the  dominant  triad  is  followed  by  some  other  chord  than  the  tonic,  the  leading-tone  may 
either  rise  or  fall,  e.g. 

(a)  <b)  (c)         ,         (d) 

I     n     I 


A    J_J     A     A     A 

ma ^ — n  -£>  — r  ij-a  - : 


V       vi        V       vi         V        it          V        II 
Although  (a)  is  usually  preferable  to  (6)  and  (c)  to  (d),  for  reasons  which  will  be  appreciated  later. 

1  The  leading-tone,  the  7th*in  the  chord  of  the  seventh,  and,  in  a  less  degree  the  3d  of 
the  triad,  may  be  called  sensitive  tones. 


HARMONY 


29 


47.  As  consecutive  Sves  and  5ths  are  nearly  always  '  the  result  of 
similar  motion,  it  is  plain  that  in  cases  where  they  would  occur  because  of 
that  motion  we  can  avoid  them  by  employing  contrary  or  oblique  motion. 
We  therefore  combine  our  statements  in  the  following  rules  for  the  connec- 
tion of  successive  triads. 

1.  IF  ONE  OR  MORE  NOTES  CAN  BE  TIED  IN  THE  SAME  VOICE  OR  VOICES 

(i.e.  the  tones  prolonged  into  the  next  chord) :  EITHER  —  TIE  WHATEVER 

NOTE    OR   NOTES    CAN    BE    TIED,    OR — LET   THE    SOPRANO,  ALTO,  AND    TENOR 
MOVE   IN   THE   OPPOSITE    DIRECTION   TO   THE    BASS.2  . 

2.  IF  NO  NOTES  CAN  BE  TIED,  THE  8\'E  AND  5TH  MUST  MOVE  IN  THE  OP- 
POSITE DIRECTION  TO  THE   BASS,  THIS     BEING  VERY    OFTEN    THE    CASE    WITH 
THE  3D   ALSO. 

3.  THE    LEADING-TONE  (WHICH   IS  ALMOST   NEVER  DOUBLED,   cf.  pp.  23, 
36)    USUALLY   ASCENDS   TO   THE   TONIC. 

It  is  obvious  (as  regards  rule  3)  that  if  the  leading-tone  would  make  consecutive 
oths  by  ascending  to. the  tonic,  it  must  descend,  contrary  to  its  usual  custom  (see  example 
(c)  following)  : 


is  somewhat 
better       ( 
than 


1  Consecutive  Sves  and  5ths  can  also  occur  in  contrary  motion,  being  then  open  to 
the  same  objection  as  in  similar  motion  (but  see  the  top  line  of  p.  74,  and  p.  242).  A 
unison  followed  by  an  8ve,  or  8ve  followed  by  unison,  produces  the  same  effect  (p.  24)  as 
consecutive  Sves. 


1  In  writing  exercises  it  is  well  to  indicntc  that  a  tone  in  kept  in  the  same  voice  in 
two  successive  chords  by  writing  a  tie  connecting  the  two  notes;  in  playing  exercises  dis- 
regard the  ties. 


30 


HARMONY 


48.  In  example  (a)  contrary  motion  is  indicated  for  the  succession 
ii- V.  It  is  not  a  point  of  great  consequence;  the  reason  for 'this  prefer- 
ence lies  mainly  in  the  two  consecutive  major  3ds  which  would  otherwise 
result  between  alto  and  tenor.  The  interval  Et?-A,  comprising  three  whole 
steps , 


is  called  a  XttJIQJiE.  the  use  of  which  was  formerly  forbidden  ;  although  such  a  rule  is  need- 
lessly rigid,  there  is  no  question  but  that  the  tritone  demands  expert  handling.  In  this  particu- 
lar case  we  can  justly  say  that  the  succession  11-  V  which  excludes  it  sounds  better  (cf.  §60.)' 

In  (b)  the  leading  tone  naturally  ascends  to  the  tonic,  in  whichever  voice  it  may  be, 
doubling  the  3d  in  vi,  in  the  succession  V-vi  (p.  41). 

In  (c)  we  see  that  the  leading  tone  may  be  forced  to  descend,  in  order  to  avoid  consecu- 
tive Stha  (in  this  case  between  soprano  and  bass). 

In  (rf)  is  an  instance  of  the  leading  tone  descending  (to  the  5th  of  the  triad),  in  order 
that  the  following  chord  may  be  complete.  This  is  often  of  good  effect  with  an  inner  voice 
(alto  or  tenor)  in  the  succession^VdL. 

At  page  253  will  be  found  additional  exercises,  supplementing  those  on  pp.^35,37t47,(>5, 
82,  92. 


1    For  a  more  complete  discussion  of  the  matter,  see  Spalding's  "  Tonal  Counterpoint, '' 
Chap  I,  §§  7-8. 


HARMONY 


31 


CHAPTER  IV 

EXERCISES   IN    TRIADS 


49.  BEFORE  proceeding  to  our  first  exercises,  in  connecting  major 
triads  and  forming  musical  sentences,  it  is  necessary  to  pay  attention  to 
certain  details,  which  are  considered  in  the  following 


GENERAL    DIRECTIONS. 
At  present  we  shall  use  but  two  clefs: 


remember  always  that  we  are  dealing  ivith  four  real  voices,  soprano,  alto,  tenor,  and  bass,  and 
write  the  soprano  and  alto  in  the 


clef,  tenor  and  bass  in  the  other. 

In  making  notes  have  the  stems  of  soprano  and  tenor  to  the  right  of  the  notes,  pointed 
upward,  with  the  tails  (if  any)  turned  to  the  richt ;  the  stems  of  the  alto  and  bass  to  the  left  of 
the  notes,  pointed  downward,  with  the  tails  turned  to  the  right. 


In  the  case  of  single  notes  on  a  staff,  or  of  aeroup  written  as  a  chord  —  if  the  note  is  above  the 
middle  line,  the  stem  will  be  on  the  left,  pointed  downward,  and  if  below  the  middle  line,  on 
the  right,  pointed  upward;  with  chords,  similarly,  the  question  of  whether  most  of  the  notes 
are  above  or  below  the  middle  line  determines  the  manner  of  writing. 


Ties  are  to  be  made  as  follows,  when  two  voices  are  on  a  staff: 


i.e.,  curving  upward  when,  used  with  the  upper  notes,  anil  downward  when  used  with  the 
lower  notes. 

60.  Certain  conventional  signs  have  boon  for  a  \nn<t  time  used  to  define  the  inclining 
of  what  are  culled  liftiired  Ixuttf*  (i.e..  all  Im^M-M  other  than  triad*  in  thn  fundamental  position), 
where  the  other  voices  are  not  written  out,  and  (he  chord*  are  understood  solely  through  the 


32 


HARMONY 


figure*  and  other  ."iens  employed.  These  figured  basses  were  largely  used  in  the  organ  parts 
of  oratorio*,  etc.,  at  the  time  of  Bach  and  Handel,  and  with  their  assistance  the  player  was 
expected  to  extemporixe  a  full  organ  part. 

51.  In  this  bonk,  if  an  8  is  below  the  firtt  bas»  note  of  an  exercise,  or  there  is  no  figure, 
the  soprano  is  to  begin  on  the  8ve;  if  a  3  or  A  is  below  the  first  note,  the  soprano  begins  on  the 
3d  or  5th. 

A  S  or  B  under  a  note  indicates  that  the  3d  of  the  triad  is  to  he  chromatically  raised  a 
semitone;  this  is  done,  e.g.  with  the  dominant  triad  of  the  minor  scale. 

A  J,  b,  or  tj,  after  a  figure  placed  below  a  bass  note,  means  that  the  note  indicated  by 
the  figure  is  affected  by  that  accidental;  and  a  line  drawn  through  a  figure  (0,  etc.)  (hat  the 
note  indicated  by  that  figure  is  to  be  chromatically  raised.  Any  figures  below  a  bass  note 
mean  that  the  chord  is  to  be  constructed  by  counting  the  intervals  thus  indicated  upward 
from  the  bass.  A  figure  3  after  any  figure  or  combination  of  figures  means  that  the  chord  first 
indicated  is  followed  by  a  triad  with  the  same  bass  note  continued  a  its  root.  An  8  followed 
by  a  7  indicates  a  triad  followed  by  a  chord  of  the  7th.  A  line  —  after  a  figure  me^ns  that 
the  note  indicatecTby  that  figure  is  to  be  continued  into  the  next  chord. 

I 


6       5f 


* 


'     ' 

J. 


"         '  '  '  ^ 

(  see  chapter  on  Ttha  ) 


6        6        5 

5        4—3 


HARMONY 


33 


In  writing  the  next  following  exercises,  remember  that  when  the  bass  is  given  it  is  under- 
stood to  be  the  root  of  a  triad  (e.g.  the  note  C  implies  that  the  other  notes  of  the  chord  are 
E  and  G).  When  the  soprano  is  given  it  is  either  root,  third,  or  fifth  of  the  triad  as  the  case 
may  be;  the  bass  to  be  written  must  always  be  the  root  of  whatever  triad  is  chosen. 

52.  Write  exercises  without  the  aid  of  an  instrument.     After  writing  try  to  realize,  by 
singing  and  playing,  how  the  single  voices  move  and  sound  melodically,  as  well  as  in  relat  ion  to 
the  chords  of  which  they  form  a  part.     Also  listen  carefully  in  playing  the  exercises  over, 
that  the  ear  may  be  trained  by  degrees  to  recognize  chord  progressions  and  the  leading  of  the 
voices.     The  corrections  made  by  the  student  himself,  from  a  comparison  of  what  he  thinks 
is  the  sound  that  he  writes  down,  and  the  real  sound  that  he  afterwards  hears,  is  of  more  value 
than  any  changes  suggested  by  another  person. 

53.  Naturalness  and  simplicity  are  desirable  in  constructing  our  first  chord  progressions; 
long  skips  in  any  voices  are  to  be  avoided,  and  indeed  we  should  move  largely  step-wise,  with 
occasional  moderate  skips.     When  the  soprano  moves  over  an  arpeggio  in  repetitions  of  the 
same  chord,  the  inner  voices,  and  occasionally  the  bass,   naturally  skip,  for  that  will  be  a 
musical  leading  of  the  voices. 

To  avoid  any  misconception,  let  us  say  that  all  exercises  in  this  work  begin  and  end  on 
the  tonic  triad;  a  piece  of  music,  however,  frequently  begins  with  some  other  chord,  although 
the  final  chord  will  practically  always  be  a  tonic  triad.  (Two  cases  of  an  unusual  beginning 
aii<l  ending  are  here  given;  they  result  from  especial  reasons.  The  first  of  these  intnxluces  a 
dramatic  moment  in  the  opera;  while  in  the  second  one  the  dominant  7th  chord  ending 
the  piece  represents  an  expectation  (a  question,  as  the  title  indicates)  which  is  answered  in 
the  piece  immediately  following.  In  ordinary  music  one  has  little  to  do  with  such  things.) 

«'  Tristan  und  Isolde,"  Introduction  of  Act  II. 


'BittendeH  Kind"  (from  "  Kimlerscenen" ;  SoHi'MANS) 

-^:-  V^TT 


34 


HARMONY 


64.  These  examples  from  1  to  31  are  for  four  voices.  Open  and  close  position  are  to 
be  u.-e>l,  and  it  is  well  to  accustom  one's  self  to  change  from  one  to  the  other  in  the  same  ex- 
ercise; avoid  an  extended  use  of  tho  extreme  tones  in  any  voice,  keeping  rather  in  the  medium 
range;  be  careful  in  spacing  the  voices;  always  find  and  remember  the  8ve  and  5th  in  every 
chord,  noticing  also  whether  there  be  a  leading-tone  present. 4 

In  examples  1-7,  the  alto  and  tenor  are  to  be  added  to  the  soprano  and  bass  given.  In 
ascertaining  each  chord  count  upward  from  the  root,  the  other  tones  being  the  3d  and  5th; 
be  careful  to  observe  the  rules  given,  as  to  consecutive  8ves  and  5ths  and  the  leading-tone, 
never  allowing  voices  to  cross  each  other. 


/«-• 

—  1  1  —  -^  — 

-p.  -»  «r—  |-j=  •*-  1  «- 

&-*L^r- 

k*J  &  \Y 

M=r-if- 

E^Efe==rt=£r^£EE= 
^  tt  t=_~[^=r^ 

^5fetJ-.|,      fi|3 


^H^— -£-i 


EUJ- 


HARMONY 


35 


WlTH  EACH  CHORD  CONSIDER   THESE  POINTS  !     1.    CAN   WE   TIE?      SHALL 
WE  TIE  ?      2.    AVOID  CONSECUTIVE  8VES  AND  5THS.      3.    Is   THERE    A  LEADING 

TONE  PRESENT  ?     Only  the  roots  of  chords  are  given ;    be  sure  that  the 
soprano  begins  on  the  right  note. 

7.  Close.  Open. 

8.  Open. 


^'  1^-^  — J    •  F     — JSEfci  z=ttZz^i_^ 


-a-g 


Open—     — Close- 


18. 


:IIP 


19. 


^m  m. 


e.~\£^+    * 
— p-±£— - 


NOTE.     At  x  conxiiler  the  succession  V-vi:  at  yttmt  of  n-V;  at  X   wp  have   fhi«   point, 
thai  the  repetition  of  a  root  often  makes  it  desirable  to  get  variety  by  the  Miprauo  (or,  if  not 


36  HARMONY 

the  soprano,  the  other  voices)  moving  to  another  interval  of  the  chord;  in  Ex.  19  we  have  a 
tequence,  in  which  each  voice  must  move  with  perfect  regularity,  measure  by  measure,  i.e., 
progress  by  the  same  intervals  (the  leading-tone  being  therefore  doubled  at  one  place). 

66.  Before  harmonizing  melodies  it  is  necessary  to  say  something 
with  regard  to  the  relative  appropriateness  of  the  triads  for  use  with 
the  different  tones  of  the  scale.  Triads  I,  V,  IV,  and  vi  are  the  ones  most 
used,  ii  and  in  less  often  and  vn°  practically  never,  in  root  position,  except 
in  a  sequence  (see  Ex.  19  preceding).  Considering  these  triads  singly,  we 
shall  find  that  in  the  major  scale  those  indicated  as  follows  under  the  dif- 
ferent degrees  are  the  ones  most  often  employed,  their  relative  frequency 
being  also  shown. 


II 

f    r 

1 

«TX 

^- 

II 

vJ 

.^ 

if 

4^                     f^  - 

I 

IV 

VI 

& 

V 

II 

I 

VI 

in 

IV      V 
n        I 
in 

IV 

VI 

V 
III 

It  is  the  custom  to  denote  major  triads  by  a  large  Roman  numeral  (I), 
minor  triads  by  a  small  one  (n),  augmented  triads  by  a  large  one  with 
a  x  after  it,  and  diminished  triads  by  a  small  one  with  a  °  after  it  (IIIX, 
vii°) ;  the  augmented  triad  appears  first  with  the  minor  scale.  A  7  after 
a  Roman  numeral  means  a  chord  of  the  7th  (V  7,  in  T).  In  harmonizing 
melodies  these  signs  will  be  much  used  to  indicate  the  chords  desired  for 
particular  notes;  similarly  major  keys  will  be  indicated  by  large  letters 
(G),  and  minor  keys  by  small  ones  (e). 


CHAPTER  V 

HARMONIZING    MELODIES    IN    MAJOR    KEYS 

66.  WE  must  also  see  what  have  proved  to  be  the  best  successions 
of  triads  in  major  keys.  It  is  only  possible  to  give  an  approximate  idea 
of  the  relative  frequency  of  such,  for  individual  taste  will  in  the  end  deter- 
mine, and  the  natural  succession  will  vary  with  different  melodies,  i.e.  one 
melody  may  demand  several  repetitions  of  the  same  triad,  while  in  another 
there  may  be  none  necessary^  ^ 

I    is  followed  by  V,  IV,  VI,  m  (seldom  by  ii). 

«    "     -1_  J_    V,  VI  (    "        "  I,  m,  IV). 

ra  "       "        «  vi,  IV  (    "        "  ii,  I,  V). 

IV "       "  V,  I,  n  (    "        "  vi,  in). 

V   "        "         "       I,  -vi,  HI,  ii  (sometimes  by  IV). 

vi  "        "         "     IV,  m,  ii,  V  (seldom  by  I). 

vii°  need  not  be  considered. 
This  table  is  applicable  to  triad*  Only,  not  to  inversions. 


2O.    Close. 


HARMONY 

Open. 


37 


in  IV       II 


.23. 


T.-ITF  TIT  TV 


vi  ii  in  I 


V    ii         IV  V     vi 


25.  Open. 


in          IV 


27.  Open.       Close. 


28. 

sa 


II        VI  V 


i 
7=1  J 


T  —  -+ 

' 


29. 

Andante  sostemitn. 

If:  -r-l it^: 


ApCADELT 


.  ------ 


b=-i 1 , 1 — 1-.-|— rrr-j-       _] — |=d=       — i— q ,.  ..  L_I  _. 

•    ^^E^?-^iE  ^lEEEE^E&E^F^fe*-"  iza^E 

1  1    M    " 

CHOPIN 


3O. 


31. 


mari/Loao. 


vi    in  V 


38  HARMONY 


CHAPTER  VI 

TRIADS   IX    MINOR    KEYS 

67.  As  stated  above  (§  27),  every  major  scale  has  a  minor  scale  so  closely 
related  to  it  (consisting  of  exactly  the  same  tones  with  one  exception)  as 
to  be  called  the  Relative  Minor.  The  tonic  of  this  scale  is  always  a  minor 
third  below  the  Relative  Major,  e.g.  the  scales  of  C  major  and  a  minor  bear 
this  relationship ;  in  like  manner  G  major  and  c  minor,  F  major  and  d  minor. 
Relative  Major  and  Minor  Keys  always  have  the  same  signature,  and  the  raising 
of  the  leading-tone  is  in  every  case  to  be  indicated  in  the  music  itself;  e.g. 
Ab  major  and  /  minor  would  both  have  for  a  signature  four  flats,  and  E£}, 
the  leading-tone  of  /  minor,  would  have  to  be  written,  whenever  it  occurred.1 
The  student  is  to  write  out  for  himself  a  table  of  signatures  of  all  the  major 
and  minor  keys,  e.g. 

Major  Keys  Signature         Relative  Minor  Keys 

a  ((1  to  be  sharped) 


;  /*  e  (I)  to  be  sharped), 

etc. 

58.   The  triads  erected  on  the  successive  degrees   of   the   harmonic 
minor  scale  are  as  follows: 


v     V       VI    vi  i<> 

In  classifying  these  triads  we  find  that  there  are  two  minor  triads,  on  the 
tonic  and  sub-dominant  (i  and  iv) ;  two  major  triads,  on  the  dominant  and 
the  sixth  degree  (V  and  VI) ;  two  diminished  triads,  on  the  second  degree 
and  the  leading-tone  (n°  and  vn°),  and  one  new  and  most  distinctive  triad, 
an  augmented  one  on  the  third  degree  (III"1").  The  minor  scale  is  evidently 
richer  in  harmonic  variety  than  the  major,  as  it  has  three  dissonant  triads 
(11°,  vii°,  III4)  as  against  one  in  major  keys  (the  leading-tone  triad). 

1  Capital  letters  (C)  are  used  to  designate  major  keys,  and  snia  1  letters  in  italics  for 
minor  l.evsia  . 


HARMONY 


39 


59.  A   marked   feature   of   the   minor   scale   is   the   interval   of   an 
augmented  2d  between  the  sixth  degree  and  the  leading-tone.     Although 
this  augmented  2cTifc  often  of  great  ^effect  when  used  in  a  melodic  way, 
it  is  generally  better  avoided  in  chord-progressions,  especially  in  the  inner 
voices.     Much  more  latitude  is  allowed  on  this  point  in  instrumental  music 
than  would  be  advisable  in  unaccompanied  music  for  voices,  for  the  aug- 
mented 2d  is  somewhat  difficult  to  sing  in  tune. 

60.  In  writing  exercises  in  the  minor  mode  the  chief  new  points  to  be 
observed  are  these:  First,  the  introduction  and  resolution  of  the  three 
dissonant  triads  (11°,  III+,  vn°) ;      Second,    that  no  voice  may  move  over 
the  interval  of  an  augmented  2<1  or  4th.     The  diminished  triad  (11°)  may 
be  connected  with  the  triads  VI  and  iv,  and  almost  always  resolves  to  the 
dominant. 


We  see  now  the  importance  of  the  recommendation  as  to  the  connection 
of  ii- V  in  the  major  mode  (§  48),  i.e.  that  the  common  tone  should  rarely 
be  prolonged,  but  that  the  upper  voices  should  move  in  contrary  motion  to 
the  bass;  for  the  first  of  the  following  combinations  are  to  be  strictly  avoided 
on  account  of  the  harsh  effect  of  the  augmented  2d.  The  interval  of  a 
diminished  5th  is  vocal  and  good. 


Had. 


Good. 


Observe  that  in  the  resolution  of  this  dissonant  triad  the  bass  ascends  a  fourth.  When 
dissonant  chords  of  the  seventh  are  treated,  we  shall  see  that  the  most  natural  resolution  of 
all  dissonances  is  for  their  bass  to  ascend  a  fourth  (or,  the  same  thing,  to  dcsrend  a  fifth). 

61.  The  augmented  triad  on  the  3d  degree  (III*)  is  a  harsh  dissonance, 
and  hence  not  commonly  used  in  root-position,  except  where  a  striking  effect 
is  desired,  e.g. 


HARMONY 

WAGNER:   "Parsifal"  (Amfortas  Motive) 


*  *^v  + 

V^V     *: 

C""\  "      hi  3                    fffl                   A                •               M 

p        r        P*      II 

•  •]    I/  £J         M        W?                                                                              53             • 

-. 

^     P  —  M  —  W  p  

y  —  L' 

a 

)-vn^   o                                      "TT^" 

H  H  H 

When  so  used  its  resolution  is  generally  to  the  triad  on  the  sixth  degree; 
i.e.  the  bass  ascends  a  fourth,  e.g. 


-\  J 


4^* 


III+  VI 
but  these  resolutions  are  also  good. 


III+        11° 


III+     iv 


This  mediant  triad  and,  in  fact,  all  dissonant  triads  (those  with  a  diminished 
or  an  augmented  5th)  are  much  more  frequent  and  generally  more  effective 
as  chords  of  the  Oth.  The  augmented  triad  is  very  useful  in  this  inversion 
to  introduce  dominant  harmony,  e.g. 


I 


^ 

III+    V- 


HARMONY 


41 


62.  The  diminished  triad  on  the  leading-tone  in  the  minor  mode  (vn°), 
like  the  corresponding  triad  in  major,  is  practically  never  employed;  as  a 
chord  of  the  sixth,  however,  it  is  very  useful  and  frequent.  The  bass  is 
generally  doubled,  although  at  times  the  original  fifth  may  be  doubled 
with  good  effect,  e.g. 


II 


(at  (a)  we  see  the  bass  doubled,  and  at  (6)  the  original  fifth). 

63.  When  the  dominant  and  sub-mediant  triads  (V  and  VI)  are  con- 
nected in  the  minor  mode,  the  voices  have  to  move  along  certain  fixed  lines 
in  order  to  avoid  consecutive  5ths  and  8ves  and  the  augmented  2d.  The 
leading-tone  always  ascends  to  the  tonic  (or  descends  from  it).  Two  of  the 
upper  voices  must  move  in  contrary  motion  to  the  bass,  and  the  3d  is  always 
to  be  doubled  in  the  triad  on  the  sixth  degree,  in  four-part  writing. 


3d  doubled. 


Never 
Aug.  id. 


Very  bad. 


Poor 
Aug.  'Jd. 


Good. 


V     VI       V     VI 


When  VI  precedes  V  the  same  arrangement  of  voices  is  to  be  followed, 
e.g. 


VI 


42 


HARMONY 


64.  In  a  descending  bass  or  soprano  the  melodic  form  of  the  minor  scale  is 
ojtcn  used,  i.e.  without  the  raised  leading-tone  (§22).  This  is  a  survival  of 
the  old  Aeolian  Mode,  which  was  identical  with  our  scale  of  a  minor  with  G, 
instead  of  G$.  The  minor  seventh,  when  so  used,  is  generally  harmonized 
with  a  chord  of  the  6th,  e.g. 


65.  NOTE.  It  is  sometimes  the  case  that  a  composition  in  a  minor  key  is  ended  by  a 
single  chord  in  the  tonic  major.  This  major  3d  in  the  final  chord  has  been  long  known  by  the 
name  of  TIERCE  DE  PICAKDIE  (Picardy  3d);  it  was  much  used  by  Bach,  and  as  a  character- 
istic example  the  following  is  given,  from  his  great  G  minor  organ  fugue: 

PICARUIE  (Picardy  3d);  it  was  much  used  by  Bach,  and  as  a  characteristic  example  the  fol- 
lowing is  given,  from  his  great  G  minor  organ  fugue: 


it  will  be  referred  to  later,  in  the  chapter  on  modulation. 

Before  proceeding  to  the  exercises  that  are  to  be  written,  there  are  given  below  two 
models;  in  analyzing  them  attention  is  drawn  to  there  points,  which  must  be  considered  in 
constructing  every  chord: 

1.  Are  there  tones  that  can  be  prolonged  into  the  next  chord?     If  so,  shall  they  be 
prolonged,  or  do  we  prefer  to  use  contrary  motion  to  the  bass  ? 

2.  If  there  are  no  tones  that  can  be  prolonged,  in  which  direction  shall  the  8ve  and 
5th  go? 

3.  Is  there  a  leading-tone  in  the  chord'? 

4.  Is  there  an  augmented  interval  to  be  avoided? 


VI 


We  have  to  avoid  the  interval  of  an  augmented  2d  (measures  1-2).  In  close  position 
the  soprano  note  is  not  tied;  in  open  position  it  is,  the  tenor  then  supplying  the  necessary 
3d  in  the  following  chord  by  making  the  good  and  vocal  skip  of  a  diminished  5th  to  GJ.  Ob- 
serve in  each  measure  but  the  last  the  employment  of  contrary  motion  to  the  bass,  to  avoid 
consecutive  8ves  and  5ths;  also  the  progressions  V-VI,  and  ii°-V,  and  the  choice  of  open  and 
close  positions  in  measures  3-4. 


HARMONY 


43 


In  Exercises  1-12  the  bass  Is  given  ;  in  13-25  the  bass  is  given,  and  a  few  chords  of  the 
6th  and  6-4  chords  are  introduced ;  in  20-25  the  simple  passing  modulations  of  relative 
major  and  minor  are  introduced  ;  and  in  2G-36  we  have  exercises  for  harmonizing  melodies. 

66.  As  the  fact  that  we  have  one  augmented  triad,  and  the  inter- 
vals of  one  augmented  2d  and  two  augmented  4ths,  affects  the  matter  of 
triad-succession,  for  minor  scales  a  table  is  given  which  differs  from  that 
for  major  ones : 

i    is  often  followed  by  V,  VI,  rv,  11°,  sometimes  by  III+  (when  followed 
by  11°,  the  3d  of  i  is  usually  in  the  soprano). 


is  generally  followed  by  V, 

<«  II  II  II      -rj-r 


occasionally  by  i,  III+. 

"    n°,  iv     (see  ex- 
amples in  §  61). 


iv  '  V,  i,  11°. 

V  "  "  i,  VI,  III+,  sometimes      "  iv. 

VI  "  "iv,  "  v,  n°. 

NOTE.  The  introduction  of  a  few  inversions  (6th  and  6-4  chords)  will 
give  more  flexibility  to  our  exercises.  The  student  is  referred  for  neces- 
sary information  to  the  introductory  paragraphs  of  the  chapter  on  the 
Inversions  of  Triads.  At  present  the  bass  of  the  chord  of  the  6th  (the  3d  of 
the  original  triad,  cf.  p.  20)  is  not  to  be  doubled  in  any  case ;  in  6-4 
chords  the  bass  should  always  be  doubled.  Until  these  chords  are  quickly 
recognized,  their  notes  must  be  ascertained  by  counting  upward  from  the 
bass  the  3d  and  6th,  and  4th  and  6th  respectively. 

Modulation  is  produced  by  means  of  a  connecting  succession  of  chords 
containing  one  or  more  tones  foreign  to  the  original  key  but  belonging  to 
the  new  one  (e.g.  in  going  from  C  major  to  a  minor  we  introduce  G#,  the 
leading-tone  of  a  minor,  while  the  change  from  a  minor  to  C  major  is  made 
by  reversing  the  process,  i.e.  having  GtJ  in  place  of  G#).  Our  modulations 
here  are  passing  ones,  so  much  so  as  hardly  to  deserve  the  name,  e.g. 


67.  It  is  advised  that  a  few  exercises  with  given  ba-^s  b>>  written  for 
three  voices.  The  basses  of  Xos.  1,  ">,  fi,  S,  lo,  1:5,  14,  17.  is  (Chapter  VII) 
are  recommended.  The  following  show  how  voices  are  doubled  and  omit- 
ted. 


: 


44 


HARMONY 


CHAPTER  VII 
TRIADS:     EXERCISES  IN  MINOR  KEYS 

THE  melody  in  the  soprano  should  be  made  as  varied  and  interesting 
as  possible,  and  indeed  good  melodic  movement  in  all  the  voices  is  desirable. 

Write  in  all  necessary  accidentals.  Observe  modulations  in  Nos.  20-25. 
At  NB.  cf.  §  64. 

1.  2.     Open  posltioo- 


Ef= 
• 


3. 


8  f 

4. 

(see  §06) 


B  B  3   j  $    5J  I       9 


5. 


Open- 


-Close- 


B         50 


7. 


3  S 

8.  NB. 


S 


1 


9. 


•     ^      /9              *               *                        -.     m           ~ 

P= 

1         \ 

[      *      1 

-P  75- 

-FH  —  P— 

f2— 

U 

*   ?C 

\  —  U- 

-!  1— 

t=p= 

—  '  —  i  — 

^^~ 

of 


HARMONY 


45 


12.  Open Close. 


93  EE    ^?3 

A,— 


*  ir  0- 


3          8 


13. 


14.     ( Chant ) 


SE 


6  9 


5JJ 


15. 


A  «         A     £ 


=tofc 


3        6 


6        f 


16. 


'*~± 


r 


=P=t: 


17.    (Chant) 


II 


fit 


18. 


c 

4 

19.  KB. 

-&- 


^i^^^^pip^ 

3  5       5tl  6  g  e 

4 

20.     Open —  — Close. 

to-  f.     I        -^r  -p— ir-dl^-u  r  •  ^  -  =f^ 

p^iM=h-    =f=Ff---^    E^S       ?tef ""- 

1       -  -  -  I .  .  '  I_J 1^  -     M        ' — '^«- — ^—  • — — 

ir     -  j  •^•H ^  ^ -^ 


21.      Open 


Close 


Open 


22. 


II 


46 


HARMONY 


23. 


-*>- 


Close 


24. 


In  harmonizing  the  following  melodies,  first  ascertain  the  key  (minor)  of 
each  exercise,  and  then  the  leading-tone,  as  well  as  the  augmented  skips 
that  must  be  avoided.  Chords  of  the  6th  and  6-4  chords  are  indicated  by 
those  figures  under  the  notes;  Roman  numerals  show  in  particular  cases 
the  triads  that  should  be  used.  Triads  may  sometimes  be  repeated;  a 
triad  may  be  followed  by  one  of  its  inversions,  and  an  inversion  may  often 
be  followed  by  its  triad ;  the  leading-tone  is  always  preceded  by  an  acciden- 
tal  in  minor  kevs. 


ESgEEJEa     H       • 


g «L 


II 


28. 


VI 


31.     Open- 


HARMONY 

-Close — Open- 


47 


II 


VI 


2           * 

S?                -^ 

r 

« 

2 

fr»  l 

1 

i             r 

l 

i           F 

s? 

V-'J  '- 

l 

r 

1             1 

£ 

1           i 

s 

JlO        6                                 HI+ 
4 

1 

35. 


Lf 

>2-F- 

5* 

t^ 

Z^ 

_ 

^,0 

™ 

9 

*    4 

VI                     6 

\ 

6 
4 

II 


II 


=F*=i^  '   H 

EH^i-&f^l 


1-4;  1-5;   1-6;  2-5;  3-6;  4-2;  4-5;  5-3;  5-6;  6-2;  6-4;  are  common  successions  of  triads 
in  botli  major  and  minor  keys;  1-6-4-5  and  l-G-4-2-5  are  often  used. 


CHAPTER  VIII 

HIDDEN   OCTAVES   AND    FIFTHS 

68.  WHEN  two  voices  go  in  similar  motion  to  a  perfect  Sve  or  .r>th, 
starting  from  some  different  interval,  we  have  what  is  known  as  the  pro- 
gression of  hidden  Sves  or  5ths.  One  voice  will  necessarily  move  by  skip, 
and  sometimes  both  will  do  so. 


\- 

rrr?    rr 


48 


HARMONY 


=st 


n^TTr^T 


From  these  illustrations  we  see  the  reason  of  the  name;  one  voice  passes  over  tones  which, 
if  sounded,  would  produce  consecutive  8ves  or  5ths;  these  8ves  and  5ths,  being  passed  over 
and  not  sounded,  are  said  to  be  hidden  (or  concealed). 

Hidden  unisons  are  less  frequent,  although  they  sometimes  occur  between 
tenor  and  bass, 


or  even  between  other  voices  (cf.  §  70) . 

69.  N.B.  The  student  is  strongly  advised,  not  to  make  a  point  of  trying 
to  avoid  these  hidden  intervals.  In  the  first  place,  questionable  progressions  of 
this  sort  will  seldom  occur  if  the  chords  are  naturally  connected  in  accordance 
irith  the  given  directions;  and,  secondly,  a  good  melodic  leading  of  the  voices 
irill  justify  all  but  a  few  cases. 

§70.  It  may,  however,  be  stated  that  hidden  8ves  and  5ths  are  more  noticeable,  and 
often  poor,  when  occurring  in  the  outer  voices;  we  shall  not  meet  with  the  worst  progression 
of  this  kind,  that  of  a  7th  or  9th  followed  by  an  8ve,  until  we  come  to  chords  of  the  7th. 

A  summary  of  the  usual  statements  regarding  these  hidden  intervals '  is  given  on  page  49 ; 
in  the  following  examples,  however,  we  see  the  futility  of  constructing  rigid  rules  that  are  not 
really  observed  by  musicians. 


1  Notice  the  hidden  8ves  between  outer  parts  in  measure  1,  and  hidden  5tha  between 
outer  parts  in  measure  3  of  each    example;  also  the  two  hidden  unisons. 


HARMONY 


49 


NOTE.  A  condensation  of  the  rules  given  in  one  of  the  most  important  manuals  is  as  fol- 
lows: Hidden  8ves  are  forbidden  between  soprano  and  bass  except  when  (a)  the  bass  rises  a 
4th  (or  falls  a  5th)  either  from  dominant  to  tonic,  or  tonic  to  sub-dominant,  and  at  the  same 
time  the  soprano  moves  by  step;  or  (6)  the  second  of  the  two  chords  is  a  6-4  chord;  or  finally, 
(c)  when  the  second  chord  is  another  position  of  the  first.  They  are,  however,  allowed  between 
any  other  two  parts,  excepting  when  a  7th  or  9th  moves  to  an  8ve  in  similar  motion. 
Hidden  5ths  between  soprano  and  bass  are  forbidden  except  (a)  in  a  progression  from  the  tonic 
to  the  dominant  chord,  or  from  sub-dominant  to  tonic,  in  both  of  which  cases  the  soprano  must 
move  by  step  of  a  second;  (6)  in  a  case  like  this; 


and  finally  (c)  from  one  to  another  position  of  the  same  chord.    Hidden  oths  are  not  prohibited 
except  between  the  outer  parts. 


CHAPTER   IX 

INVERSIONS  OF  TRIADS 

Chords  of  the  6th,  and  6-4  Chord* 

71.  EVERY  triad  of  a  major  or  minor  scale  may  appear  in  inverted 
forms,  there  being  two  inversions  possible.  To  characterize  these  we  em- 
ploy the  so-called  figured  bass,  an  old  but  excellent  way  of  defining  chords 
in  speech  and  writing;  musicians  think  and  speak  of  chords  by  their  figures. 
Words  are  saved,  and  there  is  a  most  satisfactory  clearness; 


for  to  say  a  chord  of  the  Oth  on  I),  and  a  G-4  chord  on  F,  is  as  plain  as  first 
inversion  and  second  inversion  respectively. 

72.  In  determining  every  chard,  we  in  jtrartire  alifays  count  the  inlfrrals  upward  from 
the  lowest  tone.  So  in  the  following  table,  all  the  triad*  are  comjtosed  of  a  root,  3d  and  f>th;  Ihr 
first  inversions,  of  a  bass  (not  root)  3d  and  <>lh;  the  second  inversions,  of  a  bass  (not  root)  4th  and 
fith.  These  first  and  second  inversions  of  triads  are  called  "  chords  of  the  Oth  "  and  "  6-4  (six- 
four)  chords." 


50 


HARMONY 


4  4 

The  inversions  of  triads  on  various  degrees  of  the  scale  are  useful  in  modulation,  e.g. 

X      X 


0 


r 


Chords  of  the  Gth  and  6-4  chords  must  never  be  thought  of  as  triads,  hut 
as  inversions.  It  will  be  seen  later  that  their  treatment  differs  in  impor- 
tant ix)ints  from  that  used  with  triads.  Unless  this  distinction  is  sharply 
made,  the  student  is  likely  to  become  confused  in  his  mind. 


CHAPTER  X 

CHORD   OF   THE    SIXTH 

73.  IT  is  impossible  to  make  absolute  rules  with  regard  to  the  especial 
treatment  of  this  chord,  as  exceptional  cases  are  so  numerous;  there  is 
nothing  in  harmony  requiring  more  care,  judgment,  and  good  taste;  but 
examples  of  the  usual  ways  in  which  it  appears  will  be  given  and  analyzed, 
as  well  as  some  exceptions,  a  working  scheme  being  deduced  therefrom. 
What  chiefly  makes  this  chord  difficult  is  that  its  bass  is  the  3d  of  the 
original  triad,  for  it  will  be  remembered  that  in  triads  that  tone  is  com- 
paratively seldom  doubled.  The  question,  therefore,  as  to  doubling  it 
becomes  more  complicated  and  difficult  when  the  original  3d  appears  as 
the  bass  of  the  chord  of  the  Gth,  for  we  shall  see  that  we  can  no  longer 
usually  double  the  bass,  as  we  did  with  triads. 

Reserve  the  term  ROOT  for  the  bass  of  the  triad,  and  of  chords  of  the  7th  and  9th,  thinking  o) 
the  lowest  tone  of  every  inversion  as  its  BASS  simply;  e.g.  C  is  the  HOOT  of 


the  BASSES  being  E  and  G  respectively. 


HARMONY 


51 


74.  Now  these  chords  appear  in  two  ways,  either  singly  or  two  or  more 
in  succession.     Our  decision  on  the  above  point  as  to  doubling  the  bass  will 
depend  partly  on  mere  sound,  but  even  more  on  the  melodic  leading  of  the 
voices  and  the  necessity  of  avoiding  consecutive  8ves  and  oths  and  doubled 
leading-tones.     In  our  discussion  until  §  76,  the  major  scale  is  considered. 

75.  When  the  bass  of  a  chord  of  the  6th  is  the  tonic,  the  leading  of  the  voices  will  de- 
termine as  to  the  doubling. 


ill.]          ]  .     . 


M 


r 


riU=it 


i 

f-  f-  -f-  -T  *  r  f:  f  * 
i    i      i  i 


-v   M 

When  the  bass  is  the  second  degree,  the  chord,  being  an  inversion  of  the  leading-tone 
triad,1  naturally  never  doubles  the  leading-tone  except  in  a  sequence.  (See  Chapter  XV.) 
We  may  then  have  these  forms  and  others  like  them, 


When  the  bass  is  the  3d  of  the  scale,  it  is  generally  preferable  to  double  one  of  the  other 
tones,  intitmiirh  at  the  ba»»  is  the  3d  of  the  tonic  triad,  and  therefore  of  itself  stands  out  con~ 
tpicuously  at  the  one  tone  determining  the  major  or  minor  mode  for  the  time  being, 


G66666666 

although  the  melodic  leading  of  the  voices  may  result  otherwise,  e.g. 


1  It  is  in  this  inversion  that  the  leading-tone  triad  is  most  uecful,  for  we  have  «"«n  that 
as  a  triad  it  is  impracticable  in  most  circumstances. 


52 


HARMONY 
x 


S  E 


606 

When  the  bas.«  is  the  4th  of  the  scale,  we  are  guided  entirely  by  the  leading  of  the  voices, 
XXX 


g^3^ 

^Fj 

J  -^  J  j  J- 

L-*. — - — I     ^ni^^ 


J 


X 

J-J- 


^ 


6 


e 


though  it  should  be  said  that  in  minor  scales  this  chord  of  the  6th  is  more  euphonious  if 
the  bass  be  doubled,  on  account  of  the  augmented  fourth  present,  which  is  over-emphasized  by 
the  addition  of  another  dissonance,  the  diminished  5th. 


6  6 

When  the  bass  is  the  5th  of  the  scale,  the  leading  of  the  voices  will  decide; ' 


when  the  6th,  it  is  rarely  doubled  when  occurring  singly  ; 

X 


m B— m  — m — 


I  6 

and   finally,  the  bass  on  the  7th  of  the  scale  (leading-tone),  should  never  be  doubled. 

1  Notice  the  doubled  leading-tone  in  (a) ;  in  chords  of  the  6th,  the  leading-tone,  when  not 
a  root  or  3d  of  the  original  triad,  may  sometimes  be  doubled,  for  in  this  connection  it  seems  to 
lose  its  excessive  prominence. 


HARMONY 


53 


76.  In  minor  scales  the  bass  is  seldom  doubled  when  it  is  the  tonic, 
often  when  on  the  2d  degree,  often  when  on  the  3d,  usually  when  on  the 
4th,  very  often  when  on  the  5th,  often  when  on  the  6th,  never  when  on  the 
7th  degree  (leading-tone). 


^  —         __ 

J 


_ 

r 

I  rather  bet- 
J  ter  thau     (See  §75) 


8=j=>  _ 


666 


HARMONY 


CHAPTER  XI 

CHORDS   OF   THE    6TH    IN   SUCCESSION 

77.  Two  or  more  successive  chords  of  the  6th  are  often  used,  and  we 
here  note  a  marked  difference  between  them  and  triads;  for  similar  motion 
of  all  four  parts,  generally  impossible  with  triads  on  account  of  the  resulting 
consecutive  8ves  and  5ths,  is  not  uncommon  with  chords  of  the  6th. 

Examples  of  the  ordinary  ways  of  so  using  these  chords  follow. 

X  X 

(a)       X 


6        6 


: 


J 


666666 


6666 


6        6 


6        6 


HARMONY 


55 


78.  In  (a)  we  must  not  double  the  bass  of  the  second  chord  of  the  6th,  as  consccut  ivo  Sves 
would  result  between  tenor  an<l  bass;  but  should  double  the  bass  in  the  third  chord  in  order  to 
avoid  consecutive  Sves  between  soprano  and  tenor,  and  5ths  between  alto  and  tenor,  all  the 
voice*  in  this  latter  case  being  in  similar  motion:  in  (b)  this  similar  motion  is  avoided  by  the 
use  of  open  position.  In  (r)  we  have  consecutive  otlis  between  alto  and  tenor,  which  are  of 
perfectly  good  effect,  one  5th  being  diminished.  In  (rf)  is  shown  a  diatonic  scale  in  the  bass 
with  consecutive  chords  of*the  6th,  in  which  example  we  twtire  a  cardinal  point  —  that  a 
succession  of  these  chords  is  often  used  with  the  so/irnno  a  tith  abore  the  IKIK*  and  in  similar 
motion  with  it,  the  alto  also  beinQ  in  similar  motion  and  thf  tenor  moring  alternately  up  and  ilou-n . 
Unit  auoiitina  consecutive  tires  and  ftths;  it  is  of  course  seldom  that  so  many  of  these  chords 
appear  in  succession.  The  first  chord  of  the  fith  in  (j/)  is  used  instead  of  a  triad,  so  that  there 
may  be  motion  in  one  voice  at  least  (the  bass).  In  < h)  and  (i)  we  see  that  the  melody  in  the 
soprano  determines  as  to  the  doubling,  while  in  (k)  the  bass  of  the  first  chord  of  the  fith  is 
doubled  to  avoid  consecutive  Sves  and  5ths,  although  a  different  disposition  of  the  voices 
would  render  this  doubling  unnecessary;  in  <D  we  double  to  avoid  having  too  many  roots  in 
the  bass:  in  (m)  and  (o)  the  object  is  to  have  motion  in  some  one  voice,  the  melody  in  the 
soprano  being  stationary;  in  < i>)  is  shown  that  the  IHISS  in  sometimes  doubl&i  in  bo(h  chords, 
though  not  necessarily  (soprnno  and  bass  bring  in  contrary  motion'}. 


56 


HARMONY 


79.   It  may  happen  that  the  parts  become  so  arranged  that  the  chord 
itself  sounds  poor,  further  leading  of  the  voices  also  being  difficult; 


A    j  A    4  A 


6          6 


6  66 


it  is  then  better  to  change  the  soprano  (consequently  also  the  alto  and 
tenor)  thus: 


( 


( 


6          6 


666 


the  case  is  similar  with  the  following,  in  which  the  placing  of  the  voices 
often  results  in  this  error, 


^M-f-lW 

•    — * — 


r^^^f^TT 


J: 


IJ 


i^y 


r^^f— F=f=Ep=^H 


avoidable  by  changing  from  open  to  close  position. 

tti 


r=f 


HARMONY  57 

80.  In  going  into  the  matter  with  such  minuteness  it  is  not  expected  or 
desired  that  the  student  shall  memorize  the  examples,  but  rather  use 
them  for  reference;  there  are,  however,  certain  facts  that  may  well  be 
remembered,  as  summed  up  in  the  following 

GENERAL   DIRECTIONS. 

1.  While  the  bass  of  the  chord  of  the  6th  may  be  doubled  upon  any 
degree  of  the  scale  except  7  (leading-tone),  this  occurs  most  often  on  the 
2nd  degree,  often  on  the  4th  (especially  in  the  minor  scale)  and  on  the  5th, 
but  less  so  on  1,  3  and  6. 

2.  When  there  are  successive  chords  of  the  6th ,  it  is  often  the  case 
that  the  soprano  will  proceed  in  similar  motion  with  the  bass  and  be  a  6th 
above  it;  the  other  voices  are  to  be  so  adjusted  as  to  avoid  consecutive 
8ves  and  5ths,  and  the  bass  will  be  doubled  in  every  alternate  chord  (page 
54,  (a)  (6)  (c)  (d).) 

3.  When  there  are  successive  chords  of  the  6th,  and  the  soprano  and 
bass  are  in  contrary  motion,  the  bass  will  often  (but  not  always)  be  doubled 
in  every  chord. 

~~~4.  The  bass  is  frequently  doubled  simply  to  obtain  a  better  melodic 
leading  of  the  voices;  in  this  case  a  good  progression  is  to  be  preferred  to 
a  chord  that  sounds  well,  if  there  must  be  a  choice. 


CHAPTER  XII 


81.  THIS  chord  is  used  in  but  few  ways,  and  they  can  be  definitely 
stated.  In  one  respect  it  differs  greatb'  from  the  chord  of  the  (5th,  in  that 
we  can  safely  eny  that  its  txtmi  i»  practically  alirn;/s  doubled  in  four-part 
writing.  It  is  most  often  used  on  the  accented  part  of  the  measure  in  the 
ordinary  cadence  forming  the  end  of  a  composition  or  of  a  section  of  a 
composition,  and  in  that  case  its  bass  is  the  dominant  of  whatever  key 
we  are  in;  the  chord  is  followed  by  the  dominant  triad,  this  latter 
being  often  followed  by  the  tonic  triad  of  the  same  key.  (See  Chap- 
ter XIV.) 


58 


HARMONY 


Sometimes  a  dominant  7th  chord  is  used  in  this  cadence. 


S3 


I 


J      J 


:£=£ 


0 


r  =f 

6  7 

4  ft 

NOTE.     As  the  6-4   chord,  used  in  this  way  (accented),  BO  often  means  a  cadence,  ft 
very  often  appears  as  fixing  a  modulation, 


although  the  expected  modulation  need  not  occur. 

X 


S 


j    j 


(2)  It  may  be  used  (either  on  the  accented  or  unaccented  part  of  the 
measure),  when  preceded  and  followed  by  a  triad  having  the  same  bass; 
although  this  is  rather  a  weak  progression,  and  chiefly  employed  for  variety, 
to  avoid  having  another  triad,  or  a  chord  of  the  6th. 


HARMONY 

Instead  of 

59 

or 

(6)       x 

1 

—  1  —  I  1  —  I  —  I  1  1  —  I 

yf  ^  ,^  

=d— 

—  j— 

ltnp  if1 

•     \     d  '   1    *                  • 

«   *       1      f                             *       \       SI   '       \ 

VVL>   Sml       f* 

f     1    5?  •   •    f        (•        f 

%  •    1    p       0       *    I 

1        1 

J  J 

j'      '    '    ' 

.:  AJ^_J 

T     i     i     r  '  r* 

!         1       I       1        1 

-(^-*         -9-        j        -9-        -&-• 

r-v  •      o      m          m 

•                    1    •                    m 

Im                   m     I  M 

biz  f>    P      • 

If                    P 

-  f       •       r 

Z—Ei 

«  •    1               m 

P           r  a  •    1 

(3)  Also  as  a  passing  chord  (c)  and  (eO,  in  which  case  it  is  most  likely  to  be 
unaccented. 


Notice  its  strong  cadential  effect  in  (a),  and  that  the  chord  is  weak  in  (b)  and  (c),  while 
in  (rf)  the  good  result  comes  largely  from  the  step-wise  character  of  the  bass.  In  (c)  we  should 
do  better  to  substitute  a  chord  of  the  6th. 


(4)  It  may  be  used  between  a  triad  and  a  chord  of  the  6th  of  the  same 
harmony. 


82.  It  may  be  approached  either  by  step  or  skip;  but  in  the  lattrr 
case  preat  care  is  necessary.  In  the  following  are  shown  the  most  usual 
wavs  of  its  introduction. 


GO 


HARMONY 


It  is  best  to  avoid  having  two  6-4  chords  in  succession,  although  this  can 
l>e  of  good  effect  in  some  cases  when  the  bass  moves  by  step.  Such  a  pro- 
gression as  this 


A 


etc. 


is  positively  bad  and  ugly.  In  the  following  example,  the  second  6-4  chord 
is  made  to  enter  more  naturally,  chiefly  through  the  diatonic  movement  of 
the  bass. 


etc. 


In  this  —  from  the  Third  Organ  Chorale  of  Cesar  Franck  — 

r~ 


-- 


;J— ^J=j^J-  J.J_ 

y       Jtc — hft<r~ —  fag^ —          ^ 

-&- 

j  '  >      ' 


_  J         . 

Ff 


i 


attention  is  called  to  the  same  diatonic  movement  of  the  bass,  and  also  to 


HARMONY 


61 


the  fact  that  the  distinctive  character  of  the  6-4  chord,  as  we  chiefly  meet 
with  it,  is  negatived  by  the  bass  not  being  doubled  on  any  one  of  the  three 
chords. 

NOTE.  On  page  8  of  the  score  of  Franck's  D  minor  symphony,  and  at  the  entrance  of 
the  trombones  in  the  second  movement  of  Tschaikowski's  6th  symphony,  are  instances  of 
successive  6-4  chords;  they  are  in  these  cases  separated  from  each  other  by  a  single  chord  be- 
tween, but  the  effect  is  none  the  less  singular  and  worthy  of  note.  For  an  illustration  of  these 
chords  in  succession  with  a  diatonic  bass,  the  student  is  referred  to  the  seventh  and  eighth 
measures  of  the  first  movement  of  Mozart's  C  major  symphony ;  and  for  a  discussion  of  6-1  chords 
on  various  degrees  of  the  scale,  the  sixth  chapter  of  Prout's  "  Harmony  "  should  be  consulted. 


CHAPTER  XIII 


EXERCISES   WITH    INVERSIONS   OF   TRIADS 

83.  REMEMBER  that  the  following  exercises  are  to  be  written  without  the  help  of  any 
instrument;  after  writing,  play  them  repeatedly,  listening  for  characteristic  points,  and  making 
changes  after  careful  consideration.  Play  also  the  separate  voice  parts,  to  see  whether  the 
melodic  progression  can  be  improved.  It  is  helpful  to  transpose  exercises,  and  also  to  play 
them,  reading  from  the  bass  alone;  both  of  these  things  are  at  first  difficult,  but  important  aids 
towards  clear  musical  thinking. 

As  we  are  now  dealing  with  chords  defined  by  figured  basses,  let  us  say  that  it  is  not 
enough  simply  to  calculate  the  chords  correctly  in  a  mechanical  way.  Always  try  to  obtain 
a  varied  melodic  soprano  and  bass  first  of  all,  and  then  see  how  far  the  inner  parts  may  be  made 
interesting  to  sing  and  to  hear.  Monotony  and  stiffness  are  the  worst  faults;  simple  diatonic 
step-wise  progression  is  preferable,  skips  being  used  with  discretion.  Bass  notes  without  fig- 
•res  are,  of  course,  the  roots  of  triads. 

1. 


-•!•.»»     e      « 

fj. 

3J 

J                                       ^      ,. 

9        ' 

0  •       ,\ 

S^32ZZ3I                         A     ^ 

i*4 

1 

-  -   & 

•  ; 

3         6 
2.     (Chant) 

6 

I 

6     6  —  3     6 
4  — 

6               -L^ 

i 

t  \  *  ^ 

1; 

.          i 

J  *  ^  /~* 

A         ' 

. 

&        & 

^    "  l|y 

* 

-JS— 

*j  &  — 

3 

3. 

6                         1 

666 
4 

1    ^"v  •      fa             A 

f  *~j  »  n  t>  tj- 

1                       '                   -- 

i       !  ^ 

*           *        I  (2  •             ' 

1         H  w     i 

•                   * 

™ 

'         f 

9 

T"         9 

f 

a 

4. 

6        6        e 

6        3 

4 

—  f—  i  r~r- 

6 

4 

—  i  .  —  .-,  1  _  

Bp^fzS   fa 

i  -^      ^^  i      fli 

^^&= 

^-^ 

^--y^if^ 

'        1 

3        6 

\  s^- 

6         5 

6         6          f 

v  .Lr:     *^  .L}  .vi          1 

J   • 

62 


HARMONY 


6. 


^ 


1 
I 


i 


3          6          6         f 


6          J         5J 


6          S 


66  6 

4 


666 
4 


—  ..                 —  -j 

--^'b  4  —  1  — 

-r  F— 

—  ^  — 

3  6 


6          6 
4 


66$ 
4 


8.  Open- 


3  6 


6          6 
4 


9.  Open- 

-4SL— 


-Close. 


36666 
4 


10. 


6        6 
4 


Open- 


6 
4 


12. 


>iz4: 


I      6 


13.    Close. 


II 


36656 


14.   (Chant.) 


I 


6  6 


HARMONY 


63 


-R-%ff-2-H             —  r.  r- 

£—+—<•         ? 

/       *        ' 

~1  H 

366 

6         6 

4 

6 

L-J  H 

RELATIVE   MAJOH   AND    MINOR   KEYS 
17.    Open Close. 


3      6     6 


19. 


666 


84.  In  harmonizing  melodies,  it  is  to  be  rememl>ere(l  that  especial  attention  must  be 
given  to  the  bass  (§45);  we  Hhould  try  to  have  it  melodious,  preferring  generally  movement 
by  step,  rather  than  by  skip,  and  avoiding  awkward  skips.  An  important  gain  resulting  from 
the  use  of  the  chord  of  the  Oth  is  that  we  can  do  away  with  pointless  repetitions  of  the  same 
bass  tone,  resulting  from  the  repetition  of  a  triad;  in  case  the  triad  is  repeated  in  root  position, 
the  bass  may  skip  an  8ve,  up  or  down,  with  good  effect. 


64 


HARMONY 


The  skip  of  a  6th  is  unnecessary  and  not  so  natural  as  that  of  a  3d  (measure  1  and  3-4); 
skips  of  a  7th  (measures  2,  3)  are  so  awkward  and  unvocal  that  they  must  rarely  be  used ;  the 
monotonous  repetitions  in  measures  4-5-6  can  he  improved  by  inversions;  finally  the  6  and  6-4 
chords  in  measure  7  are  excellent  examples  of  what  to  avoid,  each  being  weak  and  inappropriate 
in  this  connection. 


J.     J.     J     ^     J       ^ 


Every  note  can  form  a  part  of  three  different  triads  (but  cf.  8  46  ).  chords  of  the  6th  and 
6-4  chords;  the  one  to  be  chosen,  in  each  case,  will  depend  on  the  chords  just  preceding  and 
following.  E.G.  (Ex.  22). 


In  the  following  exercises,  certain   triads  are  indicated  by  Roman  numerals;  the  6  and  6-4 
chords  by  those  figures  in  most  cases,  though  not  always. 


nji  tt 

1 

r/  JP  Up^*                                    s% 

^^ 

• 

I 

^Q         fl      ^1^         /^ 

r     & 

r  '    i 

A 

\ 

•/JV       TJ         %t/ 

\ 

d 

&       ^ 

\S-ly 

\ 

1        I 

^•^ 

2 

6 

I 

6 

VI 

6 

6 

6 
4 

23. 


/Lb"  **    •  •              ^ 

S« 

2 

II 

Ilh       A     i            L 

J  . 

•         9          J         » 

•       >-         « 

V.p      4                  I/       | 

•      fl*         &         |J 

In  g.            6        6 

6                   VI 

26.       Close. 


Open. 


XL  Jr  v               * 

M  • 

r 

• 

r      r     1    II 

in)  ttft   1  C- 

-1  — 

—I 

i 

—  —  n 

4  —  r  n  II 

l_^t  —  Il_l  ^_ 

6 

6                     TI 

6            6 
4 

26.     Close. 


m 


? 


66666 


6         6 


Open- 


HARMONY 

Close. 


65 


^ 


VI          6  6 

4 


28. 


=£ 

=2 

P 

___£_ 

— 

—  T" 

[_ 

—  U 

--r— 

rm 

Kp     4 

—0— 

~tf»~ 

—  0  — 

—  4— 

- 

-J- 

—  «  — 

—  0— 

^•8*— 

6 

0           w 
i 

6 

6 
4 

tp 

29. 


-frfwG- 

'"•^  — 

^  - 

-*-.- 

~w~'  —  ^~f  —  w~-~ 

t-\» 

•  :             - 

*  •     » 

=r-r 

i(h   ^  a 

U 

•      0 

r    r 

2  3 

V/     " 

x 

1 

^H     ZL^M             1 

i 

4  —  v 

30.        c 

* 

G 

6         VI 

Close 

6 
4 

pen 

|              | 

0.  fr    <^ 

E, 

{3   • 

i         1 

XL  h  h  '? 

; 

*     m 

J 

CD     -i 

•     * 

•         4       _l 

m  ° 

i 

0      2. 

•       * 

6 

6 

6             6 

6    vi 

6     * 
4 

31.     Open. 


-XT.1*    )•                        fi- 

—  F-  (51  

F3= 

—  fi  —  »- 

{? 

-4^4— 

H  F  

1  1  — 

^       In  a.      6                 66                         VI                6 

85.    In  three-part  writing  the  6  and  6-4  chords  are  to  be  complete,  unless  the  leading  of 
the  voices  is  such  that  no  ambiguity  results  from  the  omission  of  a  tone  (the  chords  marked  X 
are  unmistakable.) 
X 


It  is  sometimes  the  case  that  an  inner  voice  must  move  by  a  larger  skip  than  when  four  voices 
are  at  our  disposal;  we  may  also  find  it  desirable  to  have  voices  move  over  the  intervals  of  a 
chord,  to  give  a  sense  of  completeness  (as  at  X  X). 


6       6 

4 

Tho  bashes  of  rxamples  1,  2,  3   5  B.  S.  10,  12,  13,  are  advised  for  three-part  writing;  in  thi*  the 
fii>t  rule  on  page  29  cannot  be  strictly  observed. 


66 


HARMONY 


CHAPTER  XIV 

CADENCES 

86.  THERE  are  four  cadences  in  common  use.  The  AUTHENTIC 
CADENCE  is  formed  by  the  dominant  triad  (often  with  7th  added)  fol- 
lowed by  the  tonic  triad ; 


;! 


T=F  "-r-r 

J.     A        J:     J 


r   r 


I 


v  —  i        v,  — 


f 


II 


the  strongest  form  of  this  being  preceded  by  a  6-4  chord  with  the 
dominant  for  its  bass;  the  soprano  may  end,  in  the  final  tonic  triad, 
on  either  root,  3d  or  5th. 


y  .  i?  ., 

I 

i 

• 

/rh  4-    J        J 

x> 

-4  U 

!_,  —  — 

iqr   4    >s  —  '&- 

/5 

^-  — 

—  1- 

B/  Z5/~ 

y   \ 

J             f     f 

r 

-  J 

' 

*  r 

r  f 

a       J—  J_, 

1  (7 

_ 

_^         5^ 

iO 

9^4  r  r 

—  P  — 

: 

' 

^- 

H 


6  V—  I  6         V7—  I  6          V  — I  6  V  —  I 

4444 

A  few  other  forms  follow,  in  which  the  dominant  triad  is  introduced  differ- 
ently. 


TTTf 


Lit ^ — LtT — g  I IV/    T^   a-<-< ' IV  I/ *y  I  xg L.:^ — 1__ 

^^  r^--^^^      T^T         f+"sr-v 


•*e  '- 


I 


6     V— I 


v-i 


\T7_I 


HARMONY 


67 


87.   The  PLAGAL  CADENCE  consists  of  the  sub-dominant  triad  followed 
by  tonic  triad ;  the  soprano  ending  on  root,  3d  or  5th. 


XL  h    /!»      si 

-n              1 

2 

f(T\y     V 

/5 

I       % 

D' 

S          l| 

/^<          /^ 

S3 

£  N  •      U      ,           &1 

II 

T  .  .  I/  /  »     & 

a 

J  jj    lU 

^^ 

« 

O' 

2       II 

IV   - 

-I             IV  - 

U 

-I             IV    - 

-  I 

(Observe  that  the  sub-dominant  may  appear  as  a  6-4  chord.) 

This  cadence  is  familiar  in  church  music,  being  often  used  as  an  additional  close  after  the 
Authentic  Cadence: 


V 


IV 


A  beautiful  example  of  Plagal  Cadence  in  a  major  key.  but  with  the  sub-dominant  triad  a 
minor  one,  is  in  the  very  beginning  of  Mendelssohn's  "  Midsummer  Night's  Dream  "  Overture. 
Authentic  and  Plagal  Cadences  are  called  Perfect  when  the  soprano  ends  on  the  tonic;  when  it 
is  on  the  3d  or  5th,  they  are  Imperfect. 

88.   The  HALF  CADENCE  may  in  many  cases  be  considered  as  a  sort  of 
reversal  of  the  authentic : 


for  it  ends  with  the  dominant  triad,  and  is  often  preceded  by  the  tonic  in 
6-4  position.     It  may,  however,  enter  in  other  ways,  c.y. 


68 


HARMONY 


the  usual  definition  of  it  being  that  it  consists  of  any  chord  followed  by  the  dominant  triad. 
This  cadence  may  be  fitly  compared  with  the  semi-colon  in  punctuation,  the  authentic 
resembling  the  period;  the  half  cadence  leaves  us  in  a  state  of  suspense,  for  we  feel  that  it  does 
not  mark  an  ending,  but  rather  a  pause,  or  interruption  of  the  thought.  These  two  cadences, 
from  their  property  of  balancing  each  other,  are  complementary.  The  deceptive  cadence  is 
not  unlike  a  mark  of  interrogation  (?). 

NOTE.  Some  theorists  enlarge  the  possibilities  of  this  cadence  by  admitting  that  its 
final  chord  may  have  other  degrees  of  the  scale  (11,  in,  IV,  vi)  for  its  root.  In  many  cases 
such  successions  do  have  the  especial  effect  of  the  half  cadence,  but  the  old  custom  was  to 
restrict  that  name  to  such  cadences  as  end  with  a  dominant  triad.  According  to  more  recent 
opinion,  however,  all  the  passages  in  the  following  examples  marked  by  a  X  would  be  con- 
sidered to  be  half  cadences. 

WAGNEE:  "  Tanuhauser  "  Overture 


=*e    Lrrfr^sP^  •     r-^rytyls 


(V) 


(in) 


(IV) 


(VI) 


89.  In  the  DECEPTIVE  CADENCE  the  dominant  triad ,  with  or  without  a 
7th  (often  preceded  by  the  6-4  chord,  as  in  the  authentic  cadence),  is  fol- 
lowed by  an  unexpected  chord,  which  leads  us  in  some  cases  to  a  change 
of  key.  A  number  of  specimens  are  here  given. 


HARMONY 


69 


?=v~: — ii r> i  a*    . *•  i  e*-  . =— i . «— , .  -  rU^^-r 


V7 


V7- 


(The  student  is  referred  to  the  chapter  on  the  dominant  7th  for  further 
illustration.) 

These  cadences  are  sometimes  named  differently;  but  the  terms  Authentic  and  Plapal 
are  well  established,  and  Half  Cadence  and  Deceptive  Cadence  express  what  is  meant. 
While  it  is  a  question  with  the  authentic  cadence  as  to  how  far  the  use  of  a  preceding  6-4  chord 
is  needed,  there  is  no  doubt  that  the  cadence  is  thereby  strengthened. 


CHAPTER  XV 

SEQUENCES 

90.  A  sequence  is  a  regular  and  continuous  change  of  position  of  a  definite 
group  of  notes  or  chords,  consisting  of  the  group  followed  by  at  least  tivo  such 
transpositions.  According  to  its  structure  it  will  move,  as  a  whole,  either 
upwards  or  downwards, 


and  must  progress  without  interruption  in  the  same  general  direction, 
every  interval  being  repeated  in  each  voice  identically,  although  the  differ- 
ences between  major,  minor,  augmented,  and  diminished  intervals  are  com- 
monly disregarded.  This  usual  form  of  sequence  (diatonic)  is  termed  a 
lotuil  sequence;  one  in  which  the  intervals  retain  their  quality  of  major, 
minor,  etc.,  is  called  real,  and  is  rarely  used,  being  indeed  difficult  to  man- 
age, and  often  impracticable,  so  far  as  concerns  a  good  musical  result. 


70 


HARMONY 


As  a  sequence  must  be  entirely  regular,  that  quality  in  it  is  so  im- 
portant as  to  cause  the  minor  prohibitions  against  doubled  leading-tones 
and  augmented  skips  to  be  disregarded. 


U 


91.   Sequences  are  made  much  stronger,  and  characteristic,  by  an  in- 
termixture of  dissonances  (7th  chords  and  their  inversions). 


It  will  be  noticed  in  this  last  example  that  the  dissonances  (marked  x), 
forming  an  integral  part  of  it,  make  the  sequence  inevitable,  until  it  is  finally 
given  up  in  the  seventh  measure;  for  each  dissonance,  having  its  necessary, 
and,  in  every  case,  similar  resolution,  forces  us  to  perfect  regularity.  The 
sequence  is  a  device  easily  abused,  and  care  must  be  taken  to  introduce 
it  only  where  it  really  adds  to  musical  strength  and  interest. 

It  affords  a  convenient,  pliable,  and  attractive  means  of  modulation,  by  the  possible 
chromatic  changes  in  various  tones.  In  the  last  illustration  an  Ef  introduced  in  the  fourth 
measure  would  lead  to  ft  minor,  a  G2  in  the  same  measure  perhaps  to  6  minor,  a  DJ  in  the 
sixth  measure  to  E  major. 

98.  Reference  should  be  made  to  the  figure  called  Rotalia.  This  is  practically  the  same 
as  a  sequence,  the  name  being  derived  from  an  old  Italian  popular  song,  "Rosalia,  mia  cara." 
the  melody  of  which  is  constructed  by  repeating  a  figure  several  times  in  succession,  and  trans- 


HARMONY 


71 


posing  it  a  tone  higher  at  each  reiteration;  the  figure  usually  appears  not  more  than  three 
times  in  succession  (r/.  Schumann,  "Arabeske,"  op.  18). 

93.    From  this  time  on,   the  student  is  advised  to  write  at   least  some  of  the  exer- 
cises on  four  staves,   for  the  present  being  restricted  to  the  two  clefs  thus  far  used.     In 

the  gg  clef  of  the  tenor  voice  it  is  understood  that  the  tones  are  an  8ve  lower  than  those  indi- 
cated by  the  notes. 

Written.  .    Sounding. 


(Tenor.) 


will  be  written 


— *— r=f^=*= 

*    w = 


It  will  be  well  to  begin  by  taking  some  of  the  exercises  that  have  been  previously  written 
on  two  staves,  and  to  rewrite  them  on  four  staves;  writing  entirely  on  four  staves  after  a  little 
of  this  preliminary  experience. 

The  introduction  of  especial  clefs  for  alto  and  tenor  (the  C-clefs)  will  be  made  later. 


CHAPTER  XVI 

CHORDS   OF   THE    SEVENTH 

94.  BY  adding  to  any  triad  the  tone  a  seventh  above  its  root  (§  30), 
we  obtain  a  chord  of  the  7th;  and,  as  there  are  seven  triads  in  every  major 
and  minor  scale,  we  have  seven  chords  of  the  7th  in  every  scale.  They 
differ  from  triads  and  their  inversions  in  boing  all  dissonant  chords,  varying 
in  degree  of  harshness,  by  reason  of  the  specific  kind  of  their  5ths  and  7ths 


72 


HARMONY 


r7  vn°7 

95.  Being  dissonant  they  demand  some  sort  of  resolution  in  nearly  all 
cases,  although  it  will  be  seen  later  that  it  is  possible  to  have  the  voices  so 
progress  that,  properly  speaking,  there  is  no  resolution  at  all. 

RESOLUTION  must  now  be  defined:  by  that  term  is  understood  the  chord 
follounng  the  7th  chord;  this  chord  of  resolution  may  be  consonant  or  disso- 
nant, a  full  account  of  its  possibilities  being  given  later  under  the  heading 
of  Irregular  Resolutions.  Of  these  7th  chords,  those  founded  upon  the 
dominant  (V)  and  leading-tone  (vn°)  have  a  less  pronounced  dissonant 
quality  than  the  others,  and  may  enter  in  all  circumstances  without 
preparation,  i.e.  without  the  necessity  of  either  root  or  7th  being  a  pro- 
longation of  a  tone  in  the  preceding  chord  (c/.  chapter  on  secondary  sevenths). 
As  the  one  of  which  the  dominant  is  the  root  is  far  more  used  than  any  of 
the  others,  our  first  attention  will  be  devoted  to  it. 

THE  DOMINANT  SEVENTH  CHORD 

96.  This  chord  is  composed  of  a  root,   major  3d,  perfect  5th,  and 
minor  7th,  and  has  especial  characteristics:  (1)  that  it  is  the  same  for  major 
and  minor  tonic  keys;  (2)  that  it  is  the  only  chord  so  far  discussed  that  of  itself 
defines  the  key 1  (though  not  the  mode); 


m 

PT  r  H 


and  (3)  that  it  is  therefore  much  used  in  the  authentic  cadence  (§  86). 

1  No  triad  (or  its  inversion)  defines  a  key  by  itself,  the  feeling  of  tonality  coming  from 
»  succession  of  them; 


can  be  I  in  C  major,  IV  in  G  major,    V  in  F  major  or  /  minor,  vi  in  e  minor  (and  even  III  in 
a  minor  when  form  (/)  of  the  minor  scale  is  used,  §  22).     But  with 


the  note  ¥'  shows  that  there  is  no  sharp  in  the  signature,  the  B"  that  there  can  be  no  flat,  and 
the  OS  that  we  cannot  be  in  a  minor,  so  that  the  chord  must  belong  to  either  C  major  or  e 
minor.  It  should  be  stated  that  in  a  minor  key  the  accidental  chromatically  raising  the  3d 
of  the  chord  of  the  7th  is  always  written  each  time  that  it  occurs,  as  we  have  also  found  to 
be  the  case  with  triads  and  their  inversions. 


HARMONY 


73 


97.  While  there  are  various  irregular  resolutions  of  the  dominant  7th, 
we  find  such  a  preponderance  of  cases  in  which  musical  habit  and  fseling 
demand  that  the  7th  descend  one  degree  as  to  be  justified  in  laying  that 
down  as  its  ordinary  resolution. 


The  leading-tone  (forming  the  3d  of  the  chord)  when  present,  usually 
ascends  to  the  tonic',1  sometimes,  when  in  an  inner  voice,  it  descends  to  the 
5th  of  the  chord  of  resolution,  to  supply  that  desirable  interval,  which 
would  otherwise  be  lacking. 


tJ^J: 


1 


It  is  preferable,  in  this  latter  case,  to  have  the  bass  in  contrary  motion  to  the  leading-tone  and 
the  7th,  as  the  progression  of  the  voices  is  thus  made  more  symmetrical. 

And  since  through  this  resolution  of  the  7th  and  3d,  we  obtain  two  tones 
of  the  tonic  triad,  it  is  most  natural  for  the  root  of  the  7th  (ascending  a 
4th  or  descending  a  5th)  to  go  also  to  the  root  of.  that  triad.  The  5th 
(when  present,  it  being  often  omitted)  mil  naturally  descend  to  the  tonic, 
although  it  sometimes  ascends  one  degree  for  melodic  reasons. 


98.  The  root  is  frequently  doubled,  the  5th  being  then  the  tone  usu- 
ally omitted,  the  3d  less  often.  This  doubled  root,  whether  in  soprano, 
alto,  or  tenor,  must  be  nearly  always  continued  in  the  same  voice  in  the 
chord  of  resolution. 

1  Two  tones  forming  a  diminished  interval  have  a  tendency  to  converge;  those  forming 
an  augmented  interval  to  diverge. 


J  J.A  J.     _±      ±_  j~J.j~)    J  J-J  J. 


There  are  caaes,  when  we  should  naturally  double  the  root, 


where  we  may  lead  the  soprano  thus,  for  melodic  reasons 


The  3d  (leading-tone)  and  the  7th,  sensitive  tones,  stand  out  so  prominently 
that  neither  of  them  may  be  doubled.     It  is  also  preferable  not  to  double 

*  We  meet  with  an  important  point  in  this  last  illustration,  and  one  equally  so  with 
inversions  of  7th  chords.  '1  tie  hidden  8ves  resulting  from  a  7th  or  9th  progressing  to  an 
Bve  are  absolutely  bad  (§  69),  and  a  hidden  unison  formed  by  a  2<1  progressing  to  a  unison 
is  also  to  be  avoided. 


The  progressions  of  an  8ve  followed  by  a  7th  or  9th  and  of  a  unison  followed  by  a 
7th  or  2d  are  likewise  poor  in  most  cases.    (See  p.  24  .  • 


_  J 


As  similar  motion  towards  a  dissonance  is  often  undesirable,  it  is  better  to  change 
the  disposition  of  the  voices  in  (a.*  to  that  given  in  (6). 


HARMONY 


the  5th,  as  both  chords  would  then  have  one  tone  missing,  thereby  pro- 
ducing a  thin  and  poor  effect. 

I—I J- 


99.  Be  careful  about  consecutive  5ths;  the  strong  character  of  the 
7th  so  easily  obscures  the  sound  of  the  5th,  that  especial  attention  must  be 
paid  to  this  point. 


4 (3. 


T 


A 


D 


It  is  usually  the  case  that  one  of  the  two  chords,  either  that  of  the  7th  or 
of  its  resolution,  will  be  incomplete. 


Allowable. 


J  i  j. 


r 


m 


ii 


r 

It  is  allowable  to  have  all  four  voices  progress  in  similar  motion. 


; 


100.   Here  is  a  statement  of  the  ordinary  resolution  of  this  chord: 

1.  THE  7TH   REGULARLY  DESCENDS  ONE    DKGKEK. 

2.  THE    3o   (LEADING-TONE),  WHEN   PRESENT,   USUALLY  ASCENDS  TO 


76 


HARMONY 


THE  TONIC}  SOMETIMES,  WHEN  IN  AN  INNER  VOICE,  DESCENDING  TO  THE 
5TH  OF  THE  FOLLOWING  TRIAD. 

3.  THE  STH,  WHEN  PRESENT,  USUALLY  DESCENDS  TO  THE  TONIC. 

4.  THE  ROOT,  WHEN  IN  THE  BASS,  MOVES  TO  THE  TONIC;  WHEN  IN  ANOTHER 
VOICE  ALSO,  IT  IS  PROLONGED  IN  THAT  VOICE  INTO  THE  NEXT  CHORD. 

ENTRANCE  OF  THE  DOMINANT  ?TH  CHORD 

101.   The  seventh  may  (a)  be  a  prolongation  of  a  tone  from  the  pre- 
ceding chord,  (6)  enter  by  step,  (c)  enter  by  skip. 

(a)  (6)  (c) 


±3^ 


*TT 


l:. 


i=fei? 


_^J_J    JJJ^J^_ 

gfcfcj=j=f=  E|=p=pE 

•^-»-4d  H     P  n       —P^K  =£==£= 


Although  the  regular  treatment  of  this  chord  is  somewhat  inflexible,  we 
yet  have  now  obtained  some  more  material  for  our  work,  and  shall  find 
greater  variety  and  interest  in  it.  The  exercises  appropriate  to  this  sub- 
ject win  be  found  in  Chapter  XVIII.  OBSERVE  THE  CONSECUTIVE  STHS 
(BUT  ONE  OF  THEM  BEING  PERFECT)  IN  (6).  C/.  pp.  55,  107.  For  domi- 
nant 7ths  in  cadences,  see  p.  66.  The  dominant  7th  is  frequently  preceded 
by  the  dominant  triad  without  the  7th. 


CHAPTER  XVII 

PASSING   AND  AUXILIARY  TONES 

102.  WE  shall  gain  greatly  in  our  voice  parts  by  the  introduction  of  occasional  Passing 
and  Auxiliary  Tones.  Even  in  exercises  it  is  desirable  to  write  musically  and  melodically 
without  stiffness;  as  is  the  case  in  actual  composition,  these  non-harmonic  tones  interposed 
between  the  harmonic  tones  of  chords  will  prove  our  best  aid  toward  attaining  that  object. 

It  it  a  familiar  statement  that  melody  it  horizontal  (moving,  as  it  were,  in  a  line  -  ) 
and  that  chord*  are  vertical  (III). 

BEETHOVEN:  9th  Symphony 


etc. 


T8CHAIKOW8KI:  6th  Symphony 


*       ^  • 


HARMONY 


77 


SCHUMANN:  Soldatenmarsch,  Op.  68 


When  non-harmonic  tones  of  any  sort  are  introduced  in  any  voice,  the  melody  thus  produced 
becomes  naturally  more  independent  as  regards  the  chords  through  which  it  moves,  and  we 
have  a  beginning  of  contrapuntal  treatment  of  such  a  voice.  Observe  the  square-cut,  ponder- 
ous effect  of  the  following  (a),  and  the  free,  flowing  melodic  line  of  the  separate  voices  in  (6). 

"Bin'  Feste  Burg" 

AUGUST  HAUPT:  Choralbuch 


\&     -*— f IirP|F 


PASSING    TONES 

103.  By  this  term  is  meant  non-harmonic  tones  that  are  interposed  in 
any  voice  between  harmonic  tones  of  two  successive  chords;  they  may  be 
either  (a)  diatonic  or(6)  chromatic,  and  may  occur  in  any  one  of  the  four  voices. 

"'l^M   »:H 

'^"\  ff»-H 

X          X  ' 


No  skips  are  allowed,  and  no  consecutive  8ves  and  oths  may  lx>  produced. 
V 


78 


HARMONY 


AUXILIARY  TONES 

104.  An  auxiliary  tone  is  a  non-harmonic  tone  which  returns  to  that 
tone  from  which  it  started,  and  moves  at  the  distance  of  a  tone  or  semi- 
tone above  or  below:  it  will  be  of  course,  as  is  the  passing  tone,  dissonant 
from  at  least  a  part  of  the  chord  with  which  it  is  sounded.  Consecutive 
Sves  and  5ths  must  be  looked  out  for. 


It  U  not  intended  that  the  student  shall  try  to  introduce  either  passing  or  auxiliary  tones 
excepting  in  a  natural  way  and  for  the  improvement  of  the  melody;  in  many  cases  there  will 
be  successions  of  chords  where  such  tones  are  inappropriate,  or  even  incorrect.  And  it  is 
advisable,  before  using  these  ornamental  tones  in  the  exercises  that  follow,  to  go  back  to  the 
simpler  exercises  in  triads  and  their  inversions,  rewriting  a  few  of  them  in  this  manner. 


CHAPTER  XVIII 

EXERCISES    IN    CHORDS    OF   THE    DOMINANT   SEVENTH 

105.    ALL  former  rules  hold  good  as  to  (1)  consecutive  Sves  and  5ths,  (2)  lading-tone, 
(3)  augmented  skips,  (4)  doubling  of  bass  in  6  and  0-4  chords. 

1. 


O!S3  —  &•  —               —  *  —  h/9  —                        -  -?5  — 

3=33 

j      -9                             j        &        9                   j 

SE—                               '  !                                 I 

ta 

3                   7                   666 

4 

637         ^^" 

4 

nil                                                                     1 

I 

fv*«    A       1             i 

•  • 

-9'*fe±-«  -     —  4  —  •—                                   —•- 

''         II 

^4        -—  ^—       -•     J     ^     •     J     ^ 

_J__^_  J_ 

H 

6                 7 

807 

4 

HARMONY 


3  7  66$  67 

S  S  4         $ 

In  some  of  the  following  exercises  is  introduced  an  irregular  resolution  of  the  dominant 
7th  chord,  to  a  triad  on  the  6th  degree.  This  progression  is  very  common  indeed:  the  ten- 
dency lane*  (the  7th  and  leading-tone)  have  the  same  resolution  as  regularly,  the  only  differ- 
ence being  that  the  root  does  not  go  to  the  tonic  triad.  Much  of  the  stiffness  that  would 
otherwise  be  felt  is  done  away  with  by  employing  this  resolution. 
The  chord  of  the  7th  is  usually  comple*e  (p.  74  ). 

Usual. Good.  Br.d. 


667 


6          7' 


12. 


*E 


- 

^M>§ 


3  6 


«         «  7 

« 


80 


HARMONY 


Observe  that  in  Ex.  4,  6.  11,17,  19,  we  Ho  not  have  groups  of  4  and  8  measures,  but  tho«>e  of 
6;  in  Ex.  13,  1C,  we  have  groups  of  3,  with  3-meaaure  rhythm. 


.  \ 

,                  k 

, 

Ps    1 

**  ft        *Zs 

P 

J 

', 

P 

lf-4:  1  * 

—  J  —  i 

& 

-J  P 

-<  .     J    J 

'  —  1  

_!±  —  ,  
3 

~»  w  '  —            —  '  —     —  •  —  '-^  ^  —  "  —                  —  "_-|_ 

67                                                                   67 
4 

14. 


6       7 
4 


6     7 
4 


15,  Open. 


Close. 


3  7 

s 


f       6 


6      6       f 


16. 


9'    h    i        "P" 

H 

tZE-ZB                 c?                    /o                     <!» 

0 

b  v             r                                    1                  <J 

T 

J 

37                                                                           7 

f                                                                    S 

^        \                    -  ^            i             "            ^                                    1 

"""^ 

CV    d 

~     p 

I',"                     Jf^f9*                       in          St 

\  •*  b      j-  •                                     *                             ^ 

II 

t/      &/                                                          | 

6            |                      6                             S                                       6 

O        " 

-9—  V  —        —  j  —  -<2  p  £  »__  -^2  p  —     —  J  —  *  —  jf  — 
^4  —  i     —  «  —  1                                       —  p  «  —  -  —  f  f  — 

1  a_-  Lj  1  U  1  L|  1  1  1  1  L 
3667                         66;                           67 
S            f                                     4                                         4          f 

Before  writing  the  following  exercises  for  three  voices,  refer  to  the  directions  for  similar 
ones  at  the  close  of  the  chapters  on  Inversion  of  Triads:  it  is  only  necessary  to  add  here  that 
the  root  and  7th  in  the  chord  must  of  course  be  always  present,  and  that  it  is  quite  a  matter 
of  choice  whether  the  3d  or  5th  be  the  interval  omitted.  We  may  indeed  introduce  both  of 
then,  by  employing  this  device. 


HARMONY 

We  may  also  choose  between  these  two. 


81 


)    4 


*  r  r 


gf4-g- 


*F  I  5^         f       TBT 


A  model  of  three-part  writing  v/ith  dominant  7ths. 


fy+J-J  J  J  U    /J    I 

2=4_  «r.       ±3tZg 


rr 


;  ii 


6       7 

\ 


6        6 


6  7 

4 


(Observe  that  the  incomplete  6  and  6-4  chords  are  not  at  all  doubtful;  a 
passing  tone  is  used  in  measure  3,  and  an  auxiliary  tone  in  measure  4.) 
Exercises  for  three  voices. 


r^gp"^ 


3         7 


66  66  667 

4  4 


21. 


EEE±= 

ra^I 

fc 

S^^ 

. 

...  ^         w               ^^ 

{         '   •              I 

22. 


36  fl        6         C        H    7 

fl  — 


82 


HARMONY 


Exercises  in  harmonizing  a  melody  for  four  voices. 

Dominant  7th  chorda  are  indicated  by  V;  when  a  Roman  numeral  without  a  7  is  used,  it 
means  either  a  triad  or  its  inversion,  the  root  being  the  degree  given  (I,  vi,  etc.;. 

23. 


V 


V* 


24. 


26. 


IV 


vi      V? 


V? 


26. 


=± 


-+-T- 


1 


V7      VI 


V? 


,28. 


V7 


29. 


^m 


1 


InF. 
30.     Open. 


V?         vi 


Close. 


'  o 


Ia/#.  VI  I  V^ 

In  the  following  exercises  for  four  voices  no  figures  are  given:  in  nearly 
every  chord  there  is  a  choice  to  be  made,  e.g.  of  a  triad  or  chord  of  the  6th, 
a  triad  or  6-4  chord,  a  triad  or  chord  of  the  7th. 
31. 


II 


32. 


4-U-J-       |  |  ?_ J_ ,-E^p— ,-   =p 

4-i>     "     *^B  — •- 


, 


n 


33. 


+—-P 


HARMONY 


83 


TJ.  ir  r  r- 


37. 


^  •  i*  r 

'. 


- 


CHAPTER    XIX 


INVERSIONS  OF  THE  DOMINANT  /TH  CHORD 

106.    BY  inverting  this  chord,  we  obtain  the  following: 


and  to  designate  them  clearly,  count  upward,  as  usual,  from  the  baas.  As 
the  root  and  7th  of  the  original  chord  are  the  two  characteristic  tones  that  define 
it,  these  same  two  tones  are  selected  in  naming  the  particular  inversion  em- 
ployed. That  is  (with  the  chords  given  above)  C  and  B  flat  are  1  and  7  of 


84 


HARMONY 


the  dominant  7th  chord,  and  6  and  5  of  the  first  inversion,  4  and  3  of  the 
second  inversion,  and  2  and  1  of  the  third  inversion.  We  therefore  nat- 
urally always  speak  of  the  6-5  and  4-3  chords,  and  of  chords  of  the  2d 
(the  last  one  also  as  the  4-2  chord).  After  counting  the  intervals  upward 
from  the  bass,  refer  back  in  thought  to  the  original  chord  of  the  7th;  this  is 
necessary  in  order  to  be  sure  as  to  which  tone  is  the  root  and  which  the 
7th.  In  minor  keys  the  3d  of  the  7th  chord  will  of  course  be  chromati- 
cally raised  in  the  inversions  as  well. 

J- 


107.  THE  REGULAR  RESOLUTION  of  the  7th  in  these  inversions  is  the 
game  as  with  the  original  chord,  i.e.  it  descends  one  degree;  the  root, 
being  in  every  case  in  a  voice  not  the  bass,  is  prolonged  into  the  following 
chord  in  the  same  voice;  the  leading  tone  (3d)  will  ascend  to  the  tonic;  the  5th 
may  go  to  any  tone  of  the  chord  following. 


JdJglU 


•i  J  .>-J  J  J  .'  J./-J  .t-J  ,^-J  J  J. 


The  7th  may  be  prolonged  from  the  preceding  chord,  or  may  enter  by  step 
or  by  skip. 

Two  consecutive  5ths  may  be  used,  if  one  of  them  is  not  perfect  (pp. 
106-108). 


CHAPTER  XX 

SOME   SIMPLE    MODULATIONS 

108.  ANOTHER  way  of  making  our  exercises  more  helpful  and  musical 
is  afforded  by  the  introduction  of  a  few  of  the  most  usual  modulations  (§  66). 
As  we  have  enriched  our  material  by  the  addition  of  the  dominant  7th  and 
of  its  inversions,  so  much  employed  in  the  authentic  cadence  and  in  modu- 


HARMONY 


85 


lation,  it  is  right  that  we  should  now  learn  something  of  their  practical  use 
in  that  respect.  For  the  present  we  restrict  ourselves  to  the  modulations 
between  a  major  tonic  key  and  its  relative  minor  (vi),  dominant  (V),  and 
sub-dominant  (IV). 

A  modulation  is  effected  by  introducing  one  or  more  tones  found  in  the  key 
to  which  we  are  going  and  not  in  that  which  we  leave;  it  is  usually  first  indi- 
cated by  the  presence  of  the  leading-tone  of  the  new  key,  and  is  often  definitely 
fixed  by  an  authentic  cadence,1  the  latter  sometimes  including  a  6-4  chord. 

109.  In  going  from  A  major  to  its  dominant,  we  first  introduce  the 
leading-tone  of  the  new  key,  E  major,  and  confirm  the  modulation  with  an 
authentic  cadence  (with  or  without  the  7th).  In  going  from  F  major  to  its 
sub-dominant,  we  lower  the  leading-tone  a  semitone  (by  the  introduction  of 
(Et>)  thus  having  a  new  leading-tone  (A)  of  the  new  key,  B  flat  major, 
and  concluding  with  an  authentic  cadence.  In  going  from  E^  major  to  its 
relative  minor  we  introduce  the  leading  tone  (Eft)  of  the  new  key,  and  fix 
the  modulation  by  an  authentic  cadence. 


=aLJ_,J_J=j= 

o      • . m 


II 


m 


T— r 


1  The  mere  presence  of  the  leading-tone  of  another  key  does  not  of  itself  mean  a  modu- 
lation, aa  it  may  simply  indicate  a  chromatically  changed  chord. 


86  HARMONY 

A  modulation  from  V  to  I  is  the  same  as  I  to  IV,  and  from  IV  to  I  the  same 
as  I  to  V.  The  modulation  from  a  minor  key  to  its  relative  major  is 
made  by  cancelling  the  leading-tone  of  the  minor,  in  which  case  we  of 
course  have  for  a  new  leading-tone  that  of  the  new  key. 


•    m 

« 

• 

• 

• 

i 

& 

1t-\)  *• 

~ 

• 

-^j 

^~r 
j 

J 

J 

r 

j  „..* 

U 
j 

r 

Tf 

*)* 

• 

^r/ 

M  * 

•    \ 

fl* 

~s 

1        1                ! 

Z, 

,          • 

i 

f, 

r 

f  . 

> 

iv  r 

1 

J 

Mark  the  entrance  of  the  new  key  in  each  case  (writing,  e.g.  D  for  D  major, 
g  for  g  minor) ;  introduce  a  few  passing  and  auxiliary  tones. 

Before  writing  our  next  exercises,  it  is  necessary  to  say  this  about  the  progression  V7-vi  (V7-VI 
in  minor  keys)  —  that  for  the  present  it  is  to  be  used  in  root-position  alone,  and  that  it  musk 
be  complete,  i.e.  the  root  must  not  be  doubled  (§  105). 


CHAPTER  XXI 

110.  EXERCISES  with  dominant  7ths  and  their  inversions ;  the  inversions 
always  resolve  regularly,  and  the  chords  of  the  7th  likewise  (with  the  ex- 
ception of  occasional  V7-vi,  V7-VI). 


^""\**I      i*A4         ii                            A 

^ 

i  A 

0 

1     ll 

»  *  4f  ^>   ff     t3 

^ 

i 

j   r 

^n           0 

*    P  .     |X 

*^^         i*    TfU1  j'l      ^J 

c  J 

m    p 

r 

J 

A 

ff    MI  T*  ^^ 

&  .  || 

3         7 

'     ' 

2 

6 

4 
8 

2 

1        i 
6 

6    7 

4 

*     u         « 

1 

f^i 

f-v.   o              fi» 

1 

r 

!afija    '    *r 

^  •    0 

j 

Fi 

P     1*     i 

p  A  * 

J±            1        ' 

c    J 

r 

*   i        m 

1 

^ 

'  • 

1        • 

1 

3       6 
5 

1    < 

2 

6      J 
3 

V 
2 

6 

6       7 
4       S 

S  ."t 

f     S 

HARMONY 


87 


3  * 
4 
3 


f       *        6 

2 


#667 
2  4         g 


4.         Close. 


n 

t  —  * 

:  —  1— 

~*  —  r~~ 

=*=?= 

^H 

n 

=^b 

^-j^j-j-j 

i  —  n 

366 
5 


2667 


6       7 
4 


387  67  56J 


9       * 
2 


7. 


6  67 

4         fl 


66  67 

5  4 


-=t-M ^ ! 

it: 


6        7 


-  r  r 


s. 


66  67 

5  4 


6      f  2667  4  6? 

4  3fl 


10. 


PP^ 


6  6 

54 


11.     Open- 


2  6 

-Close. 


6  6267 

54  S 


26  67 

4 


88 


HARMONY 


12. 


66*6 
4          2 


13. 


»  r 


6  66*6  666$ 

542  4 


14.     Open- 


-Close 


>V9      " 

-   P4 — I — 


ffi 


6          4 


2  66  6 7 


15. 


6         |         *        6  6 

2  5 


16. 


3        6  8—7  6  6*6  f       6         6        6  7 

6  642  4 J 

3 


17.         Open- 


-Close. 


,'4 


S        6  66*6 

5  42 


6          7 
J          ( 


18.     (  Chant ) 


M:  •» 


\,.y 


& 

6  B 

4 


19. 


" 


64  6 

3  4 


3  6 

5 


c  r 


6  8 


26 


—       7 


HARMONY 


6          6 


-Close. 


22. 


m 


^=ff=f 


-I— 


626 
4 


3      6 
5 


II 


6         * 

3 


267 


2     6 


6        7 

4 


Model  of  three-part  writing:  inversions  of  dominant  Tths. 
Alleyretto.  —      ^ 


Pa-tsing  tones  in  measures  2,  4-5,  5-6,  8,  9:  auxiliary  tones  in  measures  1,  3,  7:  in  measures 
7,  8,  the  complete  chords  are  obtained  by  a  voice  moving  over  two  tones  of  the  chord,  an  ex- 
cellent resource  in  many  cases. 

The  two  upper  voices  will  necessarily  be  in  some  rases  at  a  greater  distance 
from  the  bass  than  would  lx;  advisable  in  four-part  writing;  in  every  chord 
of  the  7th  (or  inversion)  the  root  and  7th  must  l>c  present ;  use  a  few  pass- 
ing tones  . 

23.  ( Examples  23-32  nro  for  three  voice*.) 


90 


HARMONY 


4-V'      *>       •                           0     '       P           1 

_ 

^b4                                                     13 

— 

1  —  J- 

6          6 
0 


26. 


56  666 

5  4 


26. 


II 


f6          6      £t        i       C 

2 


'.      4       •  67 

4         5 


27. 


f        6 
5 


9        9 


28. 


3  66 


i 


6  f 

5 


29. 


^^ 


36  66*6fGf 

6  4 


667 

4 


30.        Chant. 


II 


3  6 

5 


31. 


II 


6  6 

6 


6  /       6 

4 


6^6  tj       6  B 

2  5 


f       6  67 

2  4     I) 


Melodies  to  be  harmonized  for  four  voices.  V7  signifies  either  a  dominant 
7th  chord  or  one  of  its  three  inversions;  our  choice  will  be  determined  by 
the  chord-succession,  i.e.,  by  considering  the  chords  preceding  and  following, 


HARMONY 


91 


for  a  good  melodic  bass  must  be  obtained.  By  a  Roman  numeral  (I,  n)  is 
understood  either  the  triad  or  one  of  its  two  inversions.  Dominant  7ths  or 
their  inversions  are  to  be  used  at  various  places  not  indicated. 


_2  t_j?-ji= 
-•---FfT  EEEEE?: 


V7  IV 


Y7VI          V7 


35. 


V 

-    36.     ( Chant ) 


IV        V7 


37.     Open- 


V7 

-Close— 


V7 


vi  V7 


38. 


V7    vi 


V7  V7 


V7 


39. 


V7 


in     vi  V7  vi  V7 


40.     Open- 


In  !7  V7 


V7 


V7 


HARMONY 


III+  IlO  V?  V7 


_p_= 

~  •—r 


III+  iv      V      iv        i      V? 


V7 


44. 


IV  V? 


V?    VI 


IV   V 


*=F 


VI 


—  •+ 


-- 

- 


| 

—  •-!- 


t-] 


II 


V7  ,,0 


iv          V     i 


In  nearly  every  measure  of  the  following  bass  melodies  to  be  harmonized 
for  four  voices,  there  are  dominant  7ths,  or  inversions  of  the  same. 
46. 


-s> — 0 

P=r^ 


HARMONY 


93 


48. 


•     f                   1 

-    ~fo 

^~ 

U5<  d 

49. 


50.  (Chant) 


II 


61. 


^ 


62.  (  Chant  ) 


ESE 


* 


— 3— 


II 
II 


63. 


4^-.-F= 

^^3 


64.  >>^ 


•66. 


In  the  above  observe  how  natural  the  successions  Y-V7  and   IV- V7 
are  (see  p.  104  also). 


CHAPTER  XXII 

IRREGULAR    RESOLUTIONS    OF   THE    DOMINANT    ?TH 

111.  CONDITIONS  arising  from  the  melodic  leading  of  the  voices,  or 
from  the  chord  following  the  dominant  7th  chord,  frequently  bring  about 
very  different  resolutions  from  the  regular  one;  for  the  7th  jn  that  chord 
(a)  may  be  prolonged  in  the  same  voice  into  the  next  chord,  (h)  may  as- 
cend, or  (c)  may  even  give  up  its  resolution,  for  the  time  or  definitively. 


HARMONY 


The  root  may  (a)  be  prolonged  into  the  next  chord,  (6)  ascend  or  descend 
to  an  interval  other  than  the  regular  one.  Illustrations  of  these  latter 
points  may  be  found  in  §116. 

112.   The  7th   may  be  continued  as  a  diatonic   tone  into  the  next 
chord : 


rn^^r  f  rTr*MrF 


^-T^^Fg^f- 


or  as  an  enharmonically  changed  tone,  a  sudden  modulation  resulting. 

'       J- 


lat: 


A 9L 

^=T 


^m 


>)• 


03 


=F=F 


±± 


+ 


1 


113.    It  may  be  resolved  upward  diatonically,  either  by  step  or  skip, 
another  voice  sometimes  taking  the  tone  to  which  the  7th  would  have  regu- 
larly resolved  (as  the  bass  takes  it  in  example  (a)) : 
(a) 


I/TV"  v    A 

• 

_    . 

m 

• 

jt 

i^r 

•^    • 

vJJ     •    4- 

• 

r      n 

* 

r 

« 

Uj 

J 

•• 

1      1      1 

1  J- 

A 

y 

i           — 
4       /*] 

r  r 

* 

-f- 

M~i  

,    A 

2 

=  H 

^^^ 


— li: 


-•— r* 


r-T"^r 
J    J    J. 


J=t 


f=^=^ 


4 


:F— -  r--*-=-P—  > — 

'^    "=T  ^ 


II 


0 


HARMONY 


95 


or  upward  chromatically. 


KTr  v   A  '  * 

V-  .  J            ^     ^ 

^    •                r               ^^ 

*    ^n 
J 

i    r  r    P~I      "i 

etc. 

J          J          J                        ,N      J 

f""V    •         1—                      1 

•          • 

f    '                                                 1 

B»    P   L%  *T      I 

f 

r  •       i*      ^      R« 

Z-  fi-C-Ixi 

S* 

114.  The  dominant  7th  chord  sometimes  abandons  its  resolution  alto- 
gether, being  followed  by  chords  that  obliterate  the  impression  which  it  has 
made  as  a  chord  of  the  7th : 

"X v^ 

-J- 


f 
J 


piffl 


m 


r 


1 


or  does  so  for  a  moment,  but  returns  and  completes  the  expected  resolution : 
x  x 


f- 


J 


II 


7  7 

or  transfers  the  7th  to  another  voice  in  the  next  chord,  the  resolution  being 
made  in  the  latter  voice. 

.! 5r 


= 


7  7 

It  may  also  transfer  its  7th  to  another  voice  in  an  inversion  of  itself:  in  fact 
several  inversions  may  be  used  in  succession  (as  is  the  case  with  triads  and 
their  inversions). 


96 


HARMONY 
x 

J=}= 


r-r 


"r  -r-rf-y 


II 


724 
3 


^ 


Another  tone  of  the  same  chord  (8ve,  5th  or  3d)  may  be  interposed  between 
the  7th  and  its  resolution. 


x     x 


"  *1         m 

fc4=*: 


J         i         ^ 


r  r 


•j:?:i 


?=e^P=M^ 


II 


115.     A  dominant  7th  chord  in  either  a  major  or  minor  key  may  pro- 
gress to  any  triad  of  its  own  key  (except  vn°). 


i 


7=3=3 F=l-t-=F— '    I         T u 


i^a 


(H) 


(in)       V     (IV)         V7     (vi) 


The  succession  V7-vi,  being  a  very  common  one,  was  spoken  of  in  §  105,  and  has  already  been 
uaed  in  our  exercises  (as  also  V'-YI  in  minor  keys). 


E^EEii 


X  X,  I  , 


V7       11°  V7      III"1"  V7       iv  V 


iv  V7     VI 


HARMONY 


97 


It  is  sometimes  stated  that  the  dominant  7th  chord  may  progress  to  any 
7th  chord  in  its  own  key;  not  all  of  these  successions,  however,  are  of 
real  value. 


Good. 


Less  usual. 


,— r  -t 

J          j     j.         J     J 


V7— II7  V7— III7  V7— IV  V7— VI7  V7— 


Good. 


i     ^ 


^fe^EEjfcH 


J 


5« f=i- 


i±^=F 


II 


V7  —  HOT       V7— III+7 


V7  —  iv7 


116.  It  may  be  resolved  into  a  dominant  7th  chord  of  another  key  (or 
its  inversion) ;  most  often  into  one  belonging  to  one  of  the  five  nearest  re- 
lated keys. 


3p=  T~T 


. 


II 


J     ^   J.     J 


r    ' 


—       F 


-  g 


—    d 


o r  — | —  | —    -  f- 


J         ^ 


II 


It  may  be  resolved  into  the  diminished  7th  chord  (or  one  of  its  inversions) 
of  another  key. 


J 

.    Q    K  

f       i 

.  -I 

HARMONY 

PFl  

J      J 

..      1 

| 

(nr^^~  ^ 

i 

& 

& 

E 

fe    K 

? 

^^1 

^--f  —  H 
F    f 

B— 

-F 

F 

«=!  H 

-fa-            ^       \^ 
1  n  1-  >5  — 

-"H- 

JL 

p  U 

^.,, 

k)^s 

(5<  gfS1  — 

-P-*- 

19  1-        t>        —  (2_ 

—  fi»— 

^ 

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y 

| 

—  F  — 

7                7 

7 

1                     7                 | 

;»                             # 

3 

7 

6 

$ 

l*    —    g  B7_c  Bb_d  B^—eb 

117.  Finally,  the  most  important  irregular  resolution  is  that  known 
as  the  Deceptive  Cadence  (§89),  the  successions  V7-vi  in  major,  V7-VI  in 
minor  being  those  most  commonly  used. 


V7— ii          V7  —  ii      V7— 6  V7— VI 

Observe  that  in  many  deceptive  cadences  of  which  the  dominant  7th 
forms  a  part,  that  chord  must  be  complete ;  for  if  the  root  be  doubled  it  will 
usually  be  the  case  that  one  of  the  voices  will  fail  to  have  a  good  progression. 


In  (a)  the  alto  would  make  consecutive  8ves  with  the  bass  if  it  ascended 
to  A,  and  we  should  have  a  second  followed  by  a  unison    in    similar 


HARMONY 


99 


motion  (§  98)  if  it  went  to  E ;  it  may,  to  be  sure,  cross  the  tenor  and  de- 
scend to  C,  but  this  is  not  to  be  recommended.  It  is  better  to  change  the 
first  chord,  thus : 


r^f 

A-'j. 


^  <~ 


[\ 


A  similar  explanation  will  suggest  itself  to  the  student  as  regards  (6),  and 
it  is  advised  that  (6)  be  rewritten,  changing  the  first  chord,  so  that  each 
voice  may  have  a  musical  and  natural  progression. 

NOTE.  We  sometimes  have  occasion  to  use  a  chord  looking  like  a  dominant  7th  (being 
composed  of  a  root,  major  3d,  perfect  5th,  and  minor  7th),  which  occurs  through  a  chromatic 
change  really  not  affecting  the  key  in  which  we  are  (§  109) ;  an  apparent  dominant  7th,  in  this 
case  looking  like  an  inversion,  may  also  result  from  the  introduction  of  a  passing  tone. 


All  of  the  above  is  intended  for  a  statement  and  for  reference,  but  is  not  to 
be  committed  to  memory.  Every  example  recommended  may  be  found 
illustrated  in  the  best  music,  and  the  student  will  find  out  by  practical  work 
which  of  these  resolutions  are  of  general  use,  for  some  of  them  are 
seldom  employed.  The  dominant  7th,  with  its  various  irregular  resolu- 
tions, is  a  most  flexible  chord. 


100 


HARMONY 


fr 
\/>* 


CHAPTER  XXIII 

118.      EXERCISES :   IRREGULAR  RESOLUTIONS  OF  THE  DOMINANT  ?TH 


-I * 


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Open 


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5. 


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4     6    6    6       7 
3  4 


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7.  Open Close. 


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66  7 

4 


HARMONY 

9.     (Observe  the  so-called  feminine  ending  of  this  example.) 


101 


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3 


td- 


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12. 


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102 


HARMONY 


18. 


3  786  7 

f-       4  f 


6    7 
4    I 


MELODIES   TO    BE    HARMONIZED 

As  before,  V7  means  either  a  dominant  7th  chord  or  one  of  its  inver- 
sions; a  Roman  numeral  (V,  in,  IIIX,  vn°)  means  a  triad  or  one  of  its  in- 
versions. 

19: 


iv 


20. 

** 


V7 


II 


IV 


21. 


Passing  tone. 


IV 


IV 


IV     V7 


22. 

Mr 


fl 


V7    VI 


VI 


23. 


?      •  .- 

*= 


In  a  V7 


11°    IH+ 


24. 


m 


VT 


25.     (Chant) 


In  j^. 


VI 


HARMONY 


103 


f/T\V            ,0 

PJ 

z 

>^ 

E 

« 

InB* 


yr 


In  gr. 


26.    (Chant) 
J 


n     /j>  '^           ^ 
5__S 1 


In  A. 


XI    "ft        "P" 

«<?         j 

-i               (?2 

^-i              ^--i 

n 

ESifl      2 

r           (C* 

«s 

e  • 

—-S 

In  A. 


27. 


V7  V 


VI  1 1 IX     V7 


28. 


E^^^ 


^j'^; L ,-    _L.  *•  M 


IV     V7 


In  A. 


In  6. 


In  A- 


HARMONY 


In  each  of  these  bass  melodies  there  are  to  be  both  regular  and  irregular 
resolutions  (cf.  p.  93). 
29. 


II 


3     'n    iv 

30.  (Chant) 


-yy^  — 

I 

10 

—ei  &  — 

^-f- 

0 

3 

u_|  1  1 

31.  Open. 
X 


^^ 


32. 


r* 


J 


33.  ^  ^— - 


34.  (Chant) 


" 


;v->  v 


i=i 


35.          Close- 


-Open- 


36. 


•  :a= 


37. 


9itt 


pp^tt 

f-[~  y          1^=13 


HARMONY 


105 


-^  n  \         J     i 

<!>  •    «       j 

»           !                               1 

~-&  —  rr 

PM-  J     e     • 

~~z~s±a                _, 

• 

1    ,    II 

• 

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40. 

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i*        A 

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CHAPTER  XXIV 


IRRKGULAR   RESOLUTIONS   OF   INVERSIONS    OF   THE    DOMINANT   SEVENTH 

119.    (!)  THE  7th  may  be  prolonged  into  the  next  chord. 


\ 

& 

4^=* 

2 

In 

|B~J—  _-3        • 

^EI3 

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J:     J. 

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r      Mr       •      tt«      | 

1       •       i  . 

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645 

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6           7 
5 

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J                      41 

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4            &                           2 

1  An  with  triads  and  their  inversions,  tlnminant  7th  chorda  and  their  inversions  are  in- 
terchaiiKeahle  one  with  another;  the  la«t  7th  rhord  or  inversion  that  ap|>^ars  must  of  course  be 
finally  resolved.  'The  case  in  mmilar  with  the  other  7th  chords,  and  with  augmented  6th 
chords,  etc.)i  «•</• 


106 


HARMONY 

BEETHOVEN:  7th  Symphony 


^ 


J  J  J  J.  4  J  J 


120.    (2)  The  7th  may  ascend  diatonically. 

(6) 
j I 


In  (a)  the  7th  in  the  alto  ascends,  abandoning  its  resolution  to  the  bass,  as  it  is  not 
desirable  here  to  double  the  bass  of  the  ensuing  chord  of  the  6th ;  in  (h)  a  useful  fact  again 
appears(see  the  note  on  p.  65)  — that  two  consecutive  5tha  are  admissible,  in  case  one  of 
them  is  not  perfect  (i.e.  is  either  diminished  or  augmented). 

NOTE.     If 


is  played,  the  effect  is  musical  and  entirely  satisfactory,  so  far  as  sound  is  concerned.  If 
the  above  consecutive  5ths  be  changed  so  that  all  are  perfect,  the  passage  cannot  be  made 
endurable,  for  there  is  no  disposition  of  the  ether  voices  possible  that  will  sufficiently  obscure 
or  soften  the  5ths. 


121.    (3)  The  7th  may  ascend  chromatically. 


HARMONY 


107 


This  last  succession  might  also  appear  in  the  following  manner,  the  soprano  being  written  in 
both  ways,  and  the  modulation  thus  definitely  shown. 


jjcfjpi    : 

!F     —f—f=*" 

w^~i  —  f=^ 

5^8 

=^=n 

p***-r   r   r- 

6           * 
5          5 

-JB  —  H 

T 

6 
4 

122.  (4)  The  inversions  may  resolve  to  dominant  7th  chords  (or 
their  inversions)  in  other  keys,  or  to  diminished  7th  chords,  or  their  inver- 
sions (Chapter  XXVIII). 


.. 

sr  r 


r 
Jid^ 


(Obterve  the  consecutive  diminithcd  5th*  in  thr  above.) 

As  regards  these  Huccessions  of  /iths,  wliere  they  arc  not  all  perfect  ones  and  we  do  not 
class  them  as  consecutive  5ths  (§  43),  th«re  have  been  various  rules  made.  But.  as  is  usually 
the  case  in  music,  it  is  really  the  question  of  what  sounds  well  that  should  decide  for  theorists. 


108 


HARMONY 


as  well  as  for  composers.  We  find  that  the  progressions  of  a  perfect  5th  followed  by  a 
diminished  one,  and  of  a  diminished  5th  followed  by  a  perfect  one,  practically  always  occur 
when  the  4-3  chord  of  the  dominant  7th  and  the  chord  of  the  6th  of  the  tonic  triad  are  em- 
ployed, as  above.  The  progression  is  less  pure  when  other  degrees  of  the  scale  are  used;  in 
the  following  it  is  better,  e.g.  to  omit  the  5th  in  the  chord  of  the  7th  (if  the  key  were  major,  we 
should  of  course  have  consecutive  Sths). 


Rather  poor. 


Better. 


123.  Successive  diminished  oths  (in  diminished  7th  chords)  may  occur 
moving  upward  or  downward,  moving  by  diatonic  or  chromatic  step,  or  by 
skip,  and  to  any  extent.  This  is,  however,  a  progression  easily  abused, 
for  the  ear  quickly  gets  tired  of  the  sound;  like  any  pronounced  flavor,  a 
little  of  it  will  go  a  long  way. 

LISZT:  "  Les  Preludes" 


=i=r-r~g=^3Ej==i 

&  «*  f*-*  -£  -  *  t*  ; 

^p 


I  8     ' 

There  are  cases  when  a  perfect  5th  may  be  followed  by  an  augmented  one, 
or  an  augmented  5th  by  a  perfect  one,  e.g. 

X        X  ,J_H_2$_^_H &_+ 


i 


li  I  I  X        X  v 

^-^-T^y^f^^^TTf^ 

cp|;=5=  —  0  TI*    1    ^—V^  — *—       — r  •  ]  -£~&~\\ 

Pfr^f^  ^^p^^^^y 


I  II  r      \ 

124.   The  progressions  V7-vr,  V7-VI    are   commonly   used   with    the 
chords  in  root  position; 

fez^Cl): 


r_vi      VT— VI        VT— VI     VT— VI 


HARMONY 


109 


with  the  6-5  chord  we  can  get  a  satisfactory  progression  in  minor  keys,  but  in  major  keys  the 
result  is  poor; 

X 


4      A  J.        Jl.        ,N     J 


the  following  (4-3  chord)  is  not  recommended;  a  better  progression  for  obtaining  the  result 
desired  can  always  be  found; 


.. 

4  464 


34 


the  chord  of  the  2d  chiefly  occurs  when  the  bass  is  moving  dtatonically,  for  such  a  melodious 
and  symmetrical  leading  of  the  voices  is  here,  as  often,  the  means  by  which  a  smooth  and 
logical  progression  is  obtained. 


110 


HARMONY 


CHAPTER  XXV 


125.    IRREGULAR    RESOLUTIONS     OF     DOMINANT    ?TH     CHORDS    AND    OF 
THEIR  INVERSIONS. 
1. 


3         76        6       $      I     * 
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3. 


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4.     Open Close. 


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5. 


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532  2 


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466 
345 


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. 

2?     C 

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676                              2        fi 
1                                                     ^ 

7                           6 

4 

r 

HARMONY 


111 


7.  Open Close. 


M 


*£=*- 


3627 

s 


8. 


^=^ 


r^~~T 


466 
345 


62  46 

3          5 


•    •  » 

1*           •         '  J           1*1            • 

—  If 

1  —  ..         J^           1  *  " 

•             L> 

4  2 


2  6 


9. 


(Passing  tone.) 


• * 


B  6          £  6  26 

4          -2  *P 


•  i.    '         m  . 

ai 

C« 

i              py 

! 

-^  b  "K                 L 

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R                     tl                   4 

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eb 


10.          Open- 


V &<— 


II 


3  66 

11.     (Chant) 


6466 
345 


:  • 


^=±4 


366 
5 


667 


9^=gE^S4=  :3^3E 

_*I±?? =fijZZ± —    1_ )g>_ C^Z^    ^       I 


^i_n 


264  6 

3  4 


4667 
3 


12. 


:9?%z§-        zJZrilizzzibr :^ JT  i^=  :«tn-z^v 


6  f 

4 


^~  H 

zr§!~     IZ*_T|: 


112 


HARMONY 


Melodies  to  be  harmonized.     (V7  has  the  same  significance  as  in  previous 
exercises.  The  harmonies  indicated  are  to  be  regarded  as  merely  suggestive.) 
13. 


14.         Close- 


In /I. 


V7  III+          VI      In  A— 


-Open- 


V7     v7 
-In/!. 


16. 


4 


V?      v7 

In  c In  g- 


InBb.  V7    V7  In  q. 


In  c. 


16. 


In /I        V7  V7  iv  V7 


In  A- 


V7    V7  IIIX 
In/1 


17. 


In  6  flat - 


VI      iv 


In  Dflat- 


V7  iv 
-In  6  flat. 


HARMONY 


18. 


IV    V? 


VI 


-Ind. 


19. 


V     IV 


InF- 


-Ind- 


t=g= 

— • — ^ — htt — • — * — j-|  -& — 


V7     V?      In  F. 
In  F.     In  B  flat. 


Ill  VI 


20. 


4=: 


5  V?        In  g. 

In  c.        III+ 


Bass  melodies  to  be  harmonized  with  regular  and  irregular  resolutions  of 
dominant  7ths  and  their  inversions. 

21. 


O     ,  XV 


IV  I 


24.       Open. 


3  IV 


114 


HARMONY 


25.     Open- 


-Close- 


6         6 


CHAPTER  XXVI 


CHORDS  OF  THE  SEVENTH  ON  THE  LEADING-TONE 

7.   In  Major  Keys 

126.  CHORDS  of  the  7th,  of  which  the  leading-tone  is  the  root,  are  like 
dominant  7th  chords,  and  differ  from  the  remaining  7th  chords,  in  never 
requiring  preparation  (c/.  Chapter  XXX) ;  the  same  is  true  of  their  inver- 
sions.    They  are,  therefore,  discussed  in  this  place,  before  the  other  second- 
ary seventh  chords  (this  class  of  chords  including  all  except  dominant 
seventh  chords).     We  first  take  up  the  leading-tone  7th  in  major  keys. 

127.  It  may  enter  by  a  prolongation  of  its  7th  from  the  preceding 
chord,  by  step  or  by  skip. 

The  regular  resolution  is  for  its  7th  to  descend  one  diatonic  tone,  its 
root  to  ascend  to  the  tonic,  its  5th  to  descend  one  diatonic  tone,  and  its  3d 
to  ascend  or  descend  according  to  circumstances.1 

l  NOTE.     As  in  every  chord  of  the  7th,  there  are  two  5ths,  when  the  soprano  has  the  7th, 


we  see  in  the  following  the  likelihood  that  in  some  cases  consecutive  5ths  may  be  care- 
lessly written;  these  can  be  avoided  by  having  (a)  the  tenor  or  alto  ascend  (doubling  the  3d 
of  the  ensuing  triad),  or  by  letting  the  tenor  skip  (making  perfectly  good  hidden  8ves  with  the 
soprano).  In  (c)  the  soprano  does  not  have  the  7th,  but  we  have  a  similar  case,  treated  in 
the  same  manner. 


HARMONY 


115 


( a )  Never. 


9fcfcS= 
^-Wrt— rC 


(6)1 


7  7 

I         (O 


=  ^  J 


J  |         JNeverj 


128.   The  7th  may  fail  to  resolve,  being  prolonged  in  the  same  voice 
into  the  next  chord. 


7676  7676 


Observe  that,  while  the  first  chord  marked  X  js  really  a  leading-tone  7th,  from  its  rela- 
tion to  the  preceding  chord,  the  second  one  so  marked  has  lost  that  character,  for  we  are  at 
that  point  modulating  to  the  relative  minor. 

129.  Although  the  root,  being  leading-tone,  has,  of  course,  a  strong 
tendency  to  ascend  to  the  tonic,  it  sometimes  ascends  to  another  degree. 


Frequent. 


_r_= 


7         4 

3 


116 


HARMONY 


130.   But  one  of  the  inversions  of  this  chord  is  in  common  use,  as  a 
real  leading-tone  7th. 


J-XJ    JI+-J-TJ 


Sometimes. 


II 


J.          J. 


I  etc. 


m 


MBKDEL88OHK:  Part-Song,  "Farewell  to  the  Forest." 

x 


The  others  may  be  used  as  passing  chords,  but  in  this  way  largely  lose  their 
character  as  leading-tone  7ths. 


&3^ 


J_J       Jlj       J       ^zJ^rjrd^A 

H-r^r-^1^^ 


j-ij-j-j-^  /  /f; 

i£§ 


117 


:^S 


gEE=*=j=i=j  A     i-  ^ 


OT 
J— J. 


^5 


•-rs>- 


I 


T 


1 


*^ 


<x 


S 


3 


II 


interval  o/  ^w  c/iord,  or  o/  zYs  inversions,  may  be  omitted  or  doubled. 


CHAPTER  XXVII 

EXERCISES   WITH    THE    LEADING   TONE   ?TH 

(T-he  x  signifies  that  the  7th  of  the  chord  is  to  be  placed  in  the  soprano.) 

131. 

1.  ^ 


^i^ 


76  76  67 

5  4 


2.         Close- 


-Open- 


^-^g^ 


0  . 


1  767 


62       6 
4  5 


667 
4 


3. 


118 

6. 


HARMONY 


:.  6 

4 


6  67 

4 


j 


7265  4 

6  3 


667 
4 


£             1         --.**- 

CVe    A                P 

»  # 

r       ,              ri 

p*frr-f-r  *\ 

P  — 

>  1 

66767  6 

4 


Melodies  to  be  harmonized.     Leading-tone  7ths  are  indicated  by  the  x. 
9. 


g^^H 


Vii07 


10. 


Open- 


-Close- 


^tmn^F^gffrn 


11. 


12. 


V7  VII07 


13. 


m 


-t—j 


E 


V7 


II 


IV 


HARMONY 


119 


Bass  melodies  to  be  harmonized,  with  at  least  one  7th  chord  on  the  leading- 
tone  (or  inversion)  in  every  exercise.     Observe  the  passing  tones  (indicated 
by  slur  ^ )  • 
14. 


16. 


I        I     r u^ —I — M^j—  *        '  '        ^-c- 


16. 


EE 


•          *- 


In  a. 


InC. 
17. 


In  a. 


^ 


r 


18. 


II 


19. 


-N-M 


120 


HARMONY 

.^llsl/C- 


CHAPTER  XXVIII 

CHORDS   OF  THE   SEVENTH   ON   THE   LEADING-TONE 

//.  In  Minor  Keys 

THE   CHORDS   OF  THE   DIMINISHED   SEVENTH 

132.  IN  minor  keys  the  7th  of  the  leading-tone  chord  of  the  7th  is  a 
diminished  one,  the  chord  being  consequently  known  as  the  diminished 
seventh  chord. 

In  major  keys  the  7th  of  the  leading-tone  7th  is  sometimes  chromatically  lowered  a 
semitone,  so  that  we  may  have  a  diminished  7th  chord  in  such  keys  also. 


It  may  also  similarly  be  the  case  that  a  passage  in  a  minor  key  ends  with  a  major  triad. 

X 


The  7th  may  enter  (a)  as  a  prolongation  from  the  preceding  chord, 
(6)  step-wise,  or  (c)  by  skip. 

The  7th  may  be  resolved  (a)  one  diatonic  semitone  downward,  (6)  be 
prolonged  into  the  next  chord,  or  (c)  occasionally  ascend.  The  root  (a) 
usually  moves  upward  to  the  tonic,  but  (b)  may  be  prolonged  into  the  next 
chord,  or  (c)  even  progress  downward  (in  which  latter  case  there  is  often  a 
modulation). 


HARMONY 


121 


:^=pj=     =tf=        pT^gq  uu—      l-J-ggq 


33 


f^f 


It  will  be  observed  that  when  the  chord  of  resolution  is  a  triad,  the  3d 
or  5th  is  often  doubled,  as  is  also  the  case  (§  127)  with  leading-tone  7th 
chords  in  major  keys. 


133.  It  ia  permissible  to  have  the  Interval  of  an  augmented  2d  in  the  following 
chord-progression;  the  reason  is  probably  that  the  leading-tone  being  present  (and  there- 
fore conspicuous) in  each  chord,  makes  that  interval  vocally  more  natural;  the  alternative 
to  this  is  obviously  similar  motion  in  all  four  parts. 


134.   All  of  the  inversions  are  useful.     No  tone  may  be  omitted  or 
doubled  in  either  the  original  chord  of  the  7th  or  any  of  its  inversions. 


«- 


6*6*6  t         6  f        (1 


122 


HARMONY 


136.  The  chord  of  the  diminished  7th  is  the  most  ambiguous  of  all 
chords,  forming  a  strong  contrast  to  the  dominant  7th  chord  in  this  respect. 
As  with  our  tempered  scale,  we  get  practically  the  same  sound  effect  from 
diminished  7th  chords  with  different  notations  (and,  therefore,  belonging 
to  different  keys),1  we  must  be  careful  how  we  write  them.  In  determin- 
ing the  key  to  which  such  a  chord  belongs,  always  look  for  the  leading- 
tone,  e.g. 


c        e  flat        /  sharp 

To  find  the  key  in  the  first  of  these,  we  ascertain-that  there  can  be  no  sharp  or  flat  in 
the  signature;  the  key  is  therefore  C  major  or  a  minor,  and  the  leading-tone,  G  sharp,  deter- 
mines that  the  latter  is  the  case. 

The  student  is  to  find  the  keys  to  which  the  following  chords  belong: 


There  naturally  are  diminished  7th  chords  on  every  degree  of  the  chromatic  scale;  they 
may  be  written  in  different  ways  enharmonically,  as  is  seen  above.  Any  dominant  7th  chord 
can  be  made  into  a  diminished  7th  chord  by  raising  its  root  chromatically. 

CONSECUTIVE   CHORDS   OF   THE    DIMINISHED   SEVENTH 

136.  Such  successions  often  occur;  the  following  examples  will  repay 
study : 

BACH  :  Chromatic  Fantasie 


BEETHOVEN:  Sonata,  Op.  10,  No.  3 


1  This  chord,  therefore,  furnishes  an  easy  and  effective  means  of  modulation;  too 
obvious,  indeed,  for  it  has  been  used  with  such  frequency,  both  in  and  out  of  season,  that 
the  freshness  which  it  once  had  has  now  been  pretty  well  lost.  In  Spohrwe  have  a  conspicuous 
instance  of  a  composer  whose  work  was  weakened  by  the  excessive  use  of  diminished  7ths. 


HARMONY 


123 


BEETHOVEN:  Quartet  (Op.  59,  No.  1) 


— ^ft  .ftw 


WAGNER:  "Tannhauser"  Overture 


etc. 


-»•          i    i    i    '    r^     x 


137.  A  diminished  7th  chord  or  one  of  its  inversions  may,  in  some 
circumstances,  be  preceded  or  followed  (a)  by  the  same  or  another  dimin- 
ished 7th  chord  or  one  of  its  inversions,  (b)  by  a  dominant  7th  chord  or  one 
of  its  inversions,  or  (c)  by  a  secondary  chord  of  the  7th  chord,  or  one  of  its 
inversions  (the  secondary  7th  chords  very  rarely  in  root  position). 


124 


HARMONY 


Fp 

J-  J_J_J_ J^JMUJ-J-J-^LJ-  -V 

— »v       _  -  — El^..  ^  ^ T      ^  • 


138.  The  diminished  7th  chord  is  sometimes  approached  in  modulation 
in  such  a  way  that  a  so-called  cross-relation  is  made;  this,  however,  is  of 
good  effect,  provided  that  there  is  a  good  leading  of  the  voices  (cf.  Ex.  2, 
6,  in  Chapter  XXIX). 


Good. 


Poor.- 


J 


> 


T 

~&—±-    -f^—i 


I  |  —  -----  p        |  |        ^  _T_/4~       i  I          .      '        I  J         li 


CHAPTER  XXIX 

139.     EXERCISES   WITH    CHORDS    OF   THE    DIMINISHED    7TH 

— •-. a — 7s~r-*-r 


S^E^H 


•4U — >5 +-. — 

-'     ?  --?-•=*= 

-^ — I 1 — I & 


3  7fl 


264 
3 


£=£ 


--tf^f=^ 


=* 


I! 


464 
31]  3 


677 


67706 
f  54 


6       6 
5 


V"-I—  -^       f3     &      f3    11 

^-,  ?p  :: 

—?—  f2       jg      -f^-^J  &*  •      f 

.  — 

36                   7 

5 

1  —  U  1  Lj  _p  L|  <$,  1  1— 

676                    7b                   6 

5                 *                    5b 

/^f        (^  • 

t-i-  h                 ft^     r 

e.    •  I  (•»     P*                             f>y      ^ 

T'.l?'  <5       «     «?  . 

*   -*>. 

HARMONY 


125 


367 
4 


6        C      &      fl     61]   6         7  70—  7 

4  5  54—  fl 

35 


366X7 
4 


7  £        6       f  66X7 

X  344  4  X 

3 


5. 


36  6$  7         6$         *       6      $      7      63 

5  24 

Passing  tones  are  indicated  by  the  slur  ^.. 


6.  Open- 


-Close- 


'       f 


iu. 


Open 


5         4 
3 


6          6 
6 


6  6 


6          7 
4 


7.    (Chant) 


? 


v*  ^   4J    <g  =g=        r  v— 

LJ; 1 1 1 — | 1 L 


7  6 

5 


*  6 

2 


6  5 


-^Vr-fr  — 

—  ^  —  b/9  — 

o 

(? 

1_|2  = 

SE6  

1  **> 

EE  —  E 

B  ^- 

,  —  (2  — 

II 


8.         Clcxie- 


-Open- 


667 

4  tl 

-Close. 


£p 


56|667673  -i 

645$  'i 


6          f       I 
4  0 


^E 


6          8         jl         79 

4        ^       eg 


-«U_ 

6          6—7 
f 


126 


9.  Close- 


HARMONY 

-Open Close  • 


'^^  1 


667  4  66776 

4Q3  4  5 


cb 


—  a 


Melodies  to  be  harmonized;  diminished  7th  chords  and  their  inversions 
are  indicated  by  the  x.  Write  these  exercises  on  four  staves;  introduce 
a  few  passing  tones. 

10.       Open 


-Close. 
X 


In  g In  d- 


In  F- 


-v— 


-In  d.     111+ 


^ 


II 


11. 


,— l-n-M- 


VI 


12. 


' 


S 


^ 


13. 


•  B =_, |_      

1 


vi     V 


14. 


II 


HARMONY 


127 


15. 


X  X 


17. 


18.     (Chant) 


In/. 


In  c. 


Iii  Ab. 
19.     (Hymn  tune) 


In/. 


5 

nt_ 


II 


fetE 


InC- 


SE^EK 


In  a. 


Bass  melodies  to  be  harmonized  with  occasional  diminished  7th  chords 
and  their  inversions.     Passing  tones  are  indicated  by  slurs. 

20. 

— «-!-*  •    _  m  ,  9    .  V~*z — 


21. 


l 


128 


HARMONY 


In  A In  ft. 


IV 


CHAPTER  XXX. 


SECONDARY  CHORDS  OF  THE  SEVENTH 

140.  ALL,  chords  of  the  7th,  whose  roots  are  on  other  degrees  of  the  scale 
than   the   dominant,  have  been   generally   classed   as   secondary  (or  col- 
lateral) 7ths;  they  were  formerly,  with  the  exception  of  the  leading-tone 
7th,1  considered  to  be  subject  to  a  rigid  rule  as  regards  their  entrance  (the 
so-called  preparation),  this  rule  holding  good  with  their  inversions  also. 

The  strict  observance  of  this  academic  rule  has  for  a  long  time  been  dis- 
regarded by  composers;  it  should  be  remembered  that  rules  of  harmony 
worthy  of  bBsWvSrrce"  have  been  gradually  deduced,  during  the  evolution  of 
modern  music,  from  what  has  been  actually  written.  The  music  does  not 
spring  from  the  rules,  but  the  really  important  laws  (better  that  word  than 
rules)  ever  remain  to  guide  us,  though  modified  from  time  to  time  to  meet 
the  requirements  of  later  developments. 

It  is  true  that  in  music,  as  in  other  things,  the  radical  of  to-day  is  the  conservative  of 
to-morrow;  even  our  individual  point  of  view  is  constantly  changing,  and  still  more  is  that  the 
case  from  one  generation  to  another.  There  was  a  time  when  the  dominant  7th  was  not 
allowed  to  enter  without  preparation;  other  changes  of  feeling  are  going  on  in  our  own  time, 
for  we  have  seen  e.g.  during  the  last  fifty  years  the  old  doctrine  about  cross-relations  become 
entirely  modified. 

141.  Now  it  is  true  that,  where  there  is  a  choice  in  the  matter,  a  com- 
poser may  prefer  to  prepare  such  a  7th  chord,  instead  of  introducing  it 

1  It  is  because  tho  leading-tone  7th  is  understood  by  all  theorists  to  require  no  prepara- 
tion that  it  has  been  discussed  immediately  after  the  dominant  7th;  by  some  theorists  leading- 
tone  7ths  are  not  included  among  the  secondary  7ths. 


HARMONY 


129 


freely,  —  it  is  also  the  case  that  the  chord  progression  is  often  such  that 
it  is  necessary  to  have  the  preparation,  as  otherwise  the  leading  of 
the  voices  would  be  awkward,  or  result  in  harshness.  The  point  to 
emphasize  is  simply  this,  that  by  reasonable  theorists  and  musicians  this 
rule  as  to  preparation  is  no  longer  considered  absolute,  .nor  of  sufficient  con- 
sequence to  stand  against  a  better  way  of  producing  the  result  desired,  if 
that  way  preclude  the  preparation  of  the  7th  chord.  The  course  to  be 
taken  will,  in  every  case,  depend  on  the  judgment  of  the  composer;  a  few 
hints,  however,  will  not  be  out  of  place,  even  though  no  really  definite  state- 
ment can  be  made. 


Good. 


Good. 


Fairly  Good. 


The  following  is  Riven  as  an  example  of  an  unprepared  7th,  where  the  chord  of  the  7th  is 
of  itself  less  harah,  having  the  interval  of  a  minor  7th. 


It  is,  indeed,  difficult  to  wee  why  the  secondary  7th  chords  n',  IIIT,  vi7  (in  major)  should 
be  considered  essentially  much  harsher  than  the  dominant  und  leading-tone  7ths. 

It  in  clear  from  the  above  (a)  that  the  7th  (when  without  preparation) 
enters  best  in  a  6r5  chord ;  (b)  that  contrary  motion  between  root  and  7th 
softens  the  harshness;  (r)  that  the  7th  enters  best  step-wise.  The  4-3  chord 
and  the  chord  of  the  2d  are  not  easy  to  introduce  well  without  preparation. 


130 


HARMONY 


The  statements  given  later  as  to  the  resolutions  of  these  7th  chords  hold 
good,  whether  the  chords  be  prepared  or  not. 

NOTE.  "Even  in  the  last  century  the  old  law  as  to  the  preparation  and  progression  of 
these  chords  was  often  disregarded;  and  it  would  be  absurd  to  fetter  ourselves  now  by  any 
such  rule.  Any  essential  discord  may  be  taken  without  preparation."  (From  Prout's  "Har- 
mony.") 

142.  To  illustrate  the  unrestricted  way  in  which  Tths  may  be  used  in  free  contrapuntal 
writing  this  example  is  given;  some  of  the  7ths  being  passing-tones  or  appoggiaturas. 

X  X 


fe^g^EgEE    =F^-^EE[ 

1^7— r— r-f^-^r-  !  ^ 


The  student  is  advised  to  analyze  the  first  Prelude  from  the  "Well-Tempered  Clavichord"; 
the  manner  of  showing  its  harmonic  basis  being  given  in  the  measures  quoted  below.  In  the 
fine  example  from  Wagner,  observe  which  7ths  are  prepared  and  which  are  not;  also  that  in 
the  third  measure  from  the  end  the  IV7  chord  in  C  major  is  chromatically  changed. 

BACH:  "Well-Tempered  Clavichord,"  1st  Prelude 


S 


& 


etc. 


vT    \VT°  5-T  -  x^ 

WAONEB:  1st  act  of  "Die  Meistersinger' 


HARMONY 


131 


143.  To  turn  now  to  the  old  strict  rule  as  regards  preparation:  it  will 
be  conceded  that  all  of  the  following  7th  chords  are  harsh,  when  sounded 
alone,  but  that  this  effect  is  mitigated  by  the  preparation,  through  which 
either  the  7th  or  the  root  is  prolonged  from  a  tone  in  the  preceding  chord 
( i.e.  one  of  the  two  dissonant  tones  is  prepared ) .  At  the  same  time 
there  are  differences  as  to  the  degree  of  harshness:  I7  and  IV7  being  more 
marked  in  that  way  than  the  others,  because  of  the  interval  of  a  major  7th; 
while  ii7,  in7,  and  vi7  are  smoother,  with  their  interval  of  a  minor  7th.  It 
must  not  be  understood  from  this  that  I7  and  IV7  are  less  useful,  for  that 
very  quality  of  extreme  dissonance  makes  them  perhaps  even  more  inter- 
esting factors,  as  their  resolution  is  doubly  agreeable  when  it  does  come. 

Secondary  chords  of  the  7th  in  Major  Scales. 

X 


VI' 


132 


HARMONY 


NOTE.  Observe  that  the  chord  of  the  7th  on  the  IVth  degree  of  the  major  scale  is  not 
resolved  above  in  the  same  manner  as  the  others,  the  reason  being  that  by  the  root  ascending 
a  4th  (or  descending  a  5th)  we  shall  double  the  leading-tone,  a  thing  only  tolerable  in  a  sequence. 


— n — i  ^  •      ™ W — i— -tf 


It  is  more  symmetrical  to  have  the  root  and  7th  resolve  as  above,  in  all  of  the  chords, 
the  7th  moving  downward  and  the  root  upward. 

The  rule  illustrated  in  the  foregoing  may  be  summed  up  as  follows: 
Either  THE  ?TH  is  PROLONGED  IN  THE  SAME  VOICE  FROM   THE   PRE- 
CEDING CHORD; 

Or  THE  ROOT  IS  SO  PROLONGED,  IN  WHICH  LATTER  CASE  THE  ?TH  USU- 
ALLY ENTERS  DESCENDING  BY  STEP. 


7th  Prepared. 


I    «'   -  v _  J    j~j_j   . 
f^pNf=f=]!Etll 


Root  Prepared. 


X                             1 

X 

J 

X 

J        J        J 

fcd2z2                           \ 

IJ        •      -m        J 

1 

*       *       m       II 

/L  b    *     «                           * 

9      m 

• 

f(Tv"             *         V         •         • 

*         m        m 

A 

saz    4-   «     i 

i        i        r 

i*      i*      M 

^     r  r  r 

Ic      1        ' 

0                l 

1 

1       1 

X 

r^  •    u.  >• 

&—\ 

m                    ft 

*  1  •    J]f  ^f1                               A 

t                      II 

1               A          A                       i^ 

* 

V                     m 

f     T~      i   ^       >  ^          1             i 

1         P.          -P                             t 

P      - 

F          1            P         II 

j       V-                         1                    j 

7 

-p-'P       ^^ 

7        7 

1     w 

1 
7         7 

Notice  that  in  (a)  and  (6)  the  7th  chord  is  followed  by  another  dissonance  (chord  of 
the  7th);  we  see  that  the  7th  chord  is  not  necessarily  resolved  into  a  consonance,  thereby 
acquiring  a  resting-point,  but  that  we  may  have  two  or  more  chords  of  the  7th  in  succession 
(§  U7). 

When  these  chords  are  prepared,  as  indicated  above,  this  strict  treat- 
ment of  them  results  in  something  more  rigid  than  anything  with  which  we 
have  so  far  become  acquainted,  when  their  regular  resolution  follows. 


HARMONY 


133 


144.   In  the  normal  resolution 

*      (1)    THE  ?TH  NATURALLY  DESCENDS  ONE  DEGREE; 

(2)  THE  ROOT  ASCENDS  A  4TH  (OR  DESCENDS  A  STH)  ; 

(3)  THE  THIRD  USUALLY  DESCENDS  A  3D  (BUT  IS  PROLONGED  INTO  THE 
NEXT  CHORD,  IF  THAT  BE  A  SECONDARY  CHORD  OF  THE  7TH  ALSO)  ', 

(4)  THE  STH  USUALLY  DESCENDS  ONE  DEGREE; 

(5)  THE  ROOT  MAY  BE  DOUBLED,  BUT  THE  ?TH  MUST  NEVER  BE.1 

On  examining  the  above  examples,  it  will  be  found  that  the  3d  cannot  progress  by  as. 
cending  without  producing  a  bad  leading  of  the  voices,  but  we  have  in  the  following  an  illus- 
tration of  an  upward  progression  of  the  5th,  in  which  the  effect  is  musical,  and  the  leading  ol 
the  tenor  unusually  good. 


146.   In  minor  scales  we  are  restricted  in  applying  the  usual  resolution, 
by  the  augmented  intervals; 


Bad.  Good. 


Poor.  Good.  Bad. 


Good. 


-*  EF  ^FF~6^EF^rHI 

:=|^lB^  3^E  ~{\-»~  =B_f  ^EH 

•  i         I  I  I 


,,07 


VI7 


so  that  i7  and  iv7  are  impracticable  resolved  in  this  way,  but  n07,  IIIX7, 
and  VI7  are  good  and  extremely  useful,  e.g. 


GOI.DMAUK:  "Sakuntala"  Overture 


i  * 

J        I     — =  ~r-^         i 


The  7th.  being  a  sensitive  tone,  is  unfit  for  doubling. 


134 


HARMONY 


BBAHMB:  Song, "  Minnelied  " 


NOTE.     The  'chord  of  the  7th  on  the  second  degree  often  enters  in  such  a  way  that  a 
preferable  leading  of  the  voices  is  obtained  by  omitting  its  5th. 


j        J 


^         '.  ^  I 


HO?      [  J]07 

In  a  major  key  these  5ths  would  be  consecutive  perfect  ones. 

146.   The  irregular  resolutions  are  that  — 

(a)  The  7th  may  be  prolonged  into  the  next  chord,  the  course  taken 
by  the  other  voices  also  being  changed, 


I .    i 


^=qr 


A  j  J  j 


in  which  case  the  resolution  is  either  delayed,  or  abandoned  altogether: 
(6)  it  may  sometimes  ascend, 

x 


jj__ i '  ,*->.  '    _  j r*^ 

*Stt=*=:t^£^li-- 

^^f— i — r-n r  rr__j 


7        I 


HARMONY 


135 


and  in  this  case  the  tone  to  which  it  naturally  would  have  resolved  is  taken 
by  another  voice,     (p.  94,  §113.) 

(c)  The  root  may  be  prolonged  into  the  next  chord ; 


::' 


The  root  may  ascend  by  an  interval  other  than  the  4th 


ffis^ 

=^it 

3^ 

^ 

£-\.     t_A  * 

—  ••— 
J 

—  »  — 
J 

-M 
-V  -T, 

£•-.  "4 
<-  E3    • 

•    • 

=&•- 

4^fl 

1 

LJLJ  i      r 


7     7 


A  secondary  7th  chord  may  be  preceded  by  a  dominant  7th  chord  or 
one  of  its  inversions,  by  a  diminished  7th  chord  or  one  of  its  inversions,  or 
by  another  secondary  7th  chord  (§  147)  or  one  of  its  inversions ;  it  may  also 
be  followed  by  any  one  of  those  chords.  Most  of  these  points  have  been 
illustrated  i.i  preceding  examples,  but  for  completeness  the  following  are 
also  given : 


J^i^r^^i-^^l-l 

^-'   L— 'rr=r  r  1r  r  r  p5  ' 

_  J  ,i  L 

^^M 


136 


HARMONY 


J 


rrr 
+-J-+ 


f^f=f 


i 


^E 


rr 


X          x I  »»».        , 

Ej=^M^|rJ=j=^^Si| 

^TT^^P^ f~    ^f- 


>:.? 


J-i 


r  r  T 
U 


J 


P^ 


g 


. 


^=i 


r-jfea    T  •-&- f P     I  -^ g? 

T    f      T^  r      -T- T~T      ^ 


r^^M-J  ,J_ tPJ 


a^ 


r 


f^ 


*= 


i  j  J  J 


^=P 


^ 


o 


SUCCESSIVE   CHORDS   OF   THE   SECONDARY   7TH 


147.  These  chords  of  the  7th  are  frequently  used  in  succession,  the 
result  being  good  and  strong  when  not  too  many  appear  at  one  time  (for  it 
is  easy  to  let  this  device  take  the  place  of  something  better,  that  would  de- 
mand more  thought  on  the  composer's  part).  Excepting  the  sequence, 
there  is  no  chord  progression  that  is  so  fixed  in  its  treatment  as  this;  for  it 
is  obvious,  from  the  structure  of  the  succeeding  chords,  that  there  will  in 
each  one  lie  a  7th  to  be  prepared  at  the  same  moment  that  the  7th  in  another 
voice,  which  has  just  been  prepared  in  the  preceding  chord,  is  being  resolved. 
From  the  leading  of  the  voices  it  will  also  be  the  case  that  the  root  will  be  doubled 
in  every  alternate  chord. 


^Hi^^i-Am; 


j  .-    T  ,J        '  *-* 

/,  -s         S\  } 

-jLl^     T       T    >V  1-4(l-^\\  7- 


19  /,\    6     ,1 

'">^ 


HARMONY 


137 


Notice  in  the  preceding  page  that  the  chords  of  the  7th  are  alternately  complete  and  in- 
complete; that  the  sequence  could  be  continued  indefinitely,  and  comes  to  an  end  simply  to 
make  a  rounded  musical  phrase;  it  is  seldom  that  so  many  successive  chords  of  this  kind  are 
found.  At  X  observe  the  exchange  of  the  7th  of  the  chord  from  alto  to  bass,  and  the  resulting 
final  resolution  in  the  bass  (cf.  Inversions  of  secondary  7th  chords).  (§  150) 

Whenever  these  chords  seem  too  harsh,  it  may  be  that  a  different  ar- 
rangement of  the  voices  will  mitigate  that  effect.  Do  not  be  satisfied  with 
trying  one  way,  but  write  the  succession  so  that  the  complete  chord  is  the 
first  and  third  of  the  group  and  so  on,  and  also  so  that  it  is  the  second 
and  fourth,  etc.,  and  then  compare. 

The  above  example  is  more  dissonant  written  as  follows  (a),  and  in 
(6)  we  also  see  that  the  question  of  open  or  close  position  must  be  consid- 
ered. 

(a)  (6) 

IS        I  \         I         .  I  N         I  \        I 

J=TJ=J=ri=^-J==lU+J      JN  \± 


8va. 


WAGNER:  "Die  Meistersinger"  Overture 
(VoN  BULOW'S  arrangement) 


k.  J        ,        ,        I       tempo.  ten. 

E=#^=  ~te« si  -«H  «T*— f^ 

)     •.:•'  &  9     ...:*!._  "J:i^isj -iZ.-.u- 


In  the  above  splendid  example,  the  harmonic  lia-i-  of  the  7th  chords  is  of  course  this 


138 


HARMONY 


A  great  gain  in  freedom  will  be  found  now  that  we  have  added  the 
secondary  7ths  to  our  stock  of  chords,  and  in  Chapter  XXXII  we  shall  see 
that  still  more  plasticity  is  obtained  by  employing  their  inversions  also. 

NOTE.  Passing  tones  (§  103)  may  occur  on  the  accented  parts  of  the  measure  also,  and 
are  in  this  case  called  accented  passing  tone*.  The  following  illustration  will  show  the  differ- 
ence in  effect  (0  indicating  the  passing  tones). 


Accented  and  unaccented  passing-tones  are  indicated  in  the  exercises  by  short  slurs; 
the  student  is  recommended  to  introduce  these  tones  in  moderation,  when  that  can  be  done 
with  naturalness. 


CHAPTER  XXXI 


EXERCISES   INTRODUCING   SECONDARY   ?TH   CHORDS 

148.  WRITE  at  least  some  of  the  exercises  on  four  staves.  Write  each  exercise  twice: 
first  preparing  all  the  secondary  7ths,  and  the  second  time  finding  out  whether  any  of  them  may 
well  enter  without  preparation,  then  comparing  the  two  versions.  When  there  are  successive 
chorda  of  the  7th,  find  the  arrangement  of  voices  by  which  the  alternate  chords  will  sound 
best. 


\J 


fj 


-J..  v  m 

<>            _J 

r           ^ 

/*}               f3 

Z             i 

-*  b   V     « 

_           0 

r 

r        r 

J 

•                               i—  —  |—  -—  •                     ^/ 

37                     7                          26                           67 

4 

-Of  fr-tr-i 

-  i   i   .   r- 

—  i  —  -A  

=P^^~ 

B    J*     j 

,      *  - 

•     4 

•        J 

V    *        V 

"2 

• 

» 

J   J  1,1        , 

3      6       7       &     2     65  ' 

^-J-     * 

I    6        6 
54        5 

<s/ 
7        6        6       tt 

HARMONY 


139 


3.     (Chant) 


~     I  g      I   ^      I    ?        f>  — T^ 


h 


II 


4.         Open- 


-Close- 


3EEH* 


r-t- 


3      6      6     65 

6.     (Chant) 


267       776 


=5:h* 
67 
4 


37  I        6  7         J       5$ 

7.  ( Passing  tones  are  indicated  by  slurs.) 


8    7 


7777 


8.          Open- 


ftfe=t 


3      6 
5 


•S5U^ 


7     &         67  78 

&     5 


1  6      6      61J 

2  4 


9. 


1= 


=1= 


36         777         777 


63 

4 


10. 


7777  77777*66—7 


377b 


267 


r^z   - 

7  7 


11 


140 


HARMONY 


12. 


II 


13. 


3         6          7          7 

s 


6          $ 


6766|        t        6 
4  2 


726 


14.      For  three  voices. 


.»A  p  -f — f—  =:£d  -^gJ^pz  =rii 

— •—  -^—m—9 — ^      — 3—  —  •        \ 

4  3-0     — i~-J  *W~  ^^EEB 

3677  6  677 


15. 


677 


16. 


76  626  677 

5 


x  4 


17. 


677 
I 


2677 


367  4.66 

5 


7666       7       f    7 
42  4  8 


Soprano  melodies  to  be  harmonized.      (Secondary  chords  of  the  7th  are 
indicated  by  the  x.) 

18.    For  four  voices. 


X    > 


In  G- 


In  C 

19.  ( Hymn-tune ) 


-In  a- 


In  F- 


P 

sB 


-in  Bb- 


HARMONY 


20.  (Hymn-tune) 


3. 


24. 


BASS    MELODIES   TO   RF,    IIAHMONIZEI) 

!    ,  -t" 


|,i. it — o i a — i — I - — i — ' —  r   i'-*                ^    [— i™"™-^"^1  -\ — |--ri 

i"-«jilti —       — ff —                 " — P —       "  ~  </ —  J~~ 

5 

25. 

^   ^     I      u    | — I  _ L  ^i   1. 1 
3 

26.  

f4)^!^*^   T"iT*iriS  JNM'  I  3t^  -2fj  M 

S:J  •- '  1*-^  •  I      •  ^F(        Td  (     •    V               _^*__  Jri.U 


HARMONY 


29. 


=G= 


f=i=  =*= 

— * — 


30.  (Hymn-tune) 


--4—-^ — F 


CHAPTER  XXXII 

INVERSIONS  OF  THE  SECONDARY  SEVENTH  CHORDS 

149.  FOR  the  use  of  these  inversion?  without  preparation,  c/.  §  141. 
If  they  are  introduced  in  accordance  with  the  stricter  rules,  we  shall  have 
the  same  preparation  of  either  7th  or  root  as  when  the  chord  is  in  its  un- 
in verted  form.  The  7th  will  have  the  same  regular  resolution  as  before, 
but  the  root  will  be  prolonged  into  the  next  chord,  being  in  an  inner  voice. 


Free  entrance,  without  preparation 


3 


US 


£^ 


143 


With  the  usual  preparation 
(a),  x 


150.  From  the  above  it  will  be  seen  that  either  (6)  the  7th  or  (o)  the 
root  may  be  prepared;  that  the  7th  regularly  descends  one  diatonic  tone. 
In  (c)  is  an  irregular  resolution,  by  which  the  7th  is  prolonged  into  the 
next  chord,  the  root  ascending  one  diatonic  tone;  in  (</)  we  see  how  these 
inversions  are  used  in  sequences.  With  all  chords  of  the  7th,  dominant, 
leading-tone,  and  secondary,  a  7th  chord  is  often  followed  by  an  inversion 
of  itself,  and  an  inversion  is  often  followed  by  the  uninverted  chord  of  the 
7th  or  by  another  inversion  of  the  same  chord ;  the  7th  is  then  transferred 
from  one  voice  to  another,  being  usually  finally  resolved  in  the  last  chord 
or  inversion.  The  chord  of  the  7th,  or  any  inversion,  may  be  repeated,  the 
7th  being  exchanged  in  a  similar  manner  from  one  voice  to  another. 


The   7th  occasionally  ascends  to   the   3d    in    the    following    tonic    chord, 
its  resolution  (prolongation)  being  taken  by  another  voice. 


144 


HARMONY 


NOTE.  Attention  must  be  called  to  a  progression  of  frequent  occurrence  with  both 
dominant  and  secondary  7th  chords,  which  demands  great  care.  The  fault  that  easily  can  be 
made  is  shown  in  the  following;  musical  and  right  ways  of  handling  the  chords  being  also 
indicated. 


-J— J.-..J-B=i=J= 


^f=t=. 
pfeE^ 


?«J    ' 


J    J-J    J 


J    J    J    J.       J    J 


6          6 
5 


6         6 
5 


EEE3 


trrH 


6        6 
5 


151.    In  the  following  illustrations  we  see  what  powerful  and   interesting  factors  the 
chord.*  of  the  7th  are,  and  how  effectively  they  may  be  used  in  succession. 

BEETHOVKX:  Sonata,  op.  2,  No.  1 


IEG:  Oaotte  from  the  Suite  "Aus  Holberg'g  Zeit" 


9-    9     3       9      .g.  -.y.     4 


HARMONY 


145 


-*+-r-*   u    *- 


etc. 


747  676 

3 


SCHUMANN:  Song,  "Ich  grolle  nicht" 


F*-  <r 


'£.  ^Y^  I    0(^ — =3 h-«  - 

•» =i— b  S      jtej  —  E^i 


-I  i       -      ,  ,     T~^  — 

__4-         I     L     |          1     b-^1     zraa — ^_^. 
4  •^^-^-•0-^.1  4  7 

37474  3 

3  3 


CHOPIN:  Prelude  (Op.  28,  No.  4) 


' 


-       4    ! 


:ffill 


^iEp^sa  •  ' . :  •  *~;  ^  r. 

=^—  %     4^  a   - 


.-! 


—v- 


146 


HARMONY 


2(vi7) 

152.  Observe  the  following  directions  faithfully.  With  a  secondary 
chord  of  the  7th,  always  be  sure  which  tone  is  the  7th  and  which  the  root;  with 
an  inversion,  count  upward  from  the  bass,  ascertaining  what  the  notes  in  the 
chord  ARE  as  the  chord  stands,  and  then  what  are  the  ?TH  AND  ROOT  OF  THE 

ORIGINAL  UNINVERTED  CHORD. 

We  have,  e.g.,  in  F^K'g —  the  notes  F-A-C-D;  the  original  chord  of  the 

6 

5 

7th  was  D-F-A-C,  D  being  the  root,  and  C  the  7th. 

Write  every  exercise  twice;  first  preparing  all  the  secondary  7ths  and 
their  inversions,  and  the  second  time  finding  out  whether  any  of  them  may 
enter  to  advantage  without  preparation;  after  this,  comparing  the  two 
versions. 


CHAPTER  XXXIII 


EXERCISES    INTRODUCING    INVERSIONS   OF   SECONDARY   SEVENTHS 
153.   (Always  find  the  root  and  7th  of  the  uninverted  chord.) 
1. 


>V            i—  k-                         J—  *         -f  P        • 

• 

~T  — 

JL_S  —  !—  ±=  L^_            -  _  l      i  L- 

36                                      6                           C                         6 
5                                      5 

P 

7 

C\*    h      (•      m                    m                                                   m             ^^ 

|        J 

gi  i 

ft                mm? 

•S    b                                                                             *                                 \  m 

J        J 

^™1'     i     i     ^j     1     r         J    J  ' 

* 

•     1:1 

x           2         6                                              76     — 
5                         6                             4      — 

8 
i 

3 

2. 


*£tte=C 
1 


3f67         466^(7b 
4  3442 

3 


6      B      7 


HARMONY 


147 


3666  4 

543 


277  676  77 

5 


i 


76 
4 


7  D     6  6  #6 

555  4  2 


-^ '  1 I 


H«.       • 


2      6 


7626767  67 

5  5 


4.          Open- 


-Close. 


2          6 


6626         46*6       7      jf 
5      4  5         3b  2 


6          6 
5          4 


67  7  67 

4        : 


iS 


3  6 67  6  7664 

5 4  5  53 


32  77 


6664 
54  3 


7  J    2    T,    f!  2      C       C        70 

:i ; 


HARMONY 


m 


F      0 


m 


7         6  4  7         * 

3  12  6» 


7  1  6 


7         *       *      6        4     6       6        6         1  1 *      7tJ     6     7fl6- 

3tJ     2  3454  2      55     4  5 


^^^=^P^p^ 


^T 


4         7fl 4          6*671 

3fl  342 


7. 


3= 


F3*-»- 


2  76  262  7*  6756$* 

555  5  1     3fl         45  4     1 2 


^3 


: 


67  61  7  71       65    6  267 

51  4; 

2 


3         6         76f*672         6         |*          7  :      »  ;      f.        r.  - 
2  5         5        3          65     3         4        3f 


*6767666J7 
2  41  15} 


7         1 


9.    ( Chant ) 


7 


e 


6  6 

5 


i    6 


I     ' 


HARMONY 


149 


SOPRANO   MELODIES    TO    BE    HARMONIZED  ^ 

(In  each  of  these  are  secondary  chords  of  the  7th  and  their  inversions;  some  of  them, 
though  not  all,  are  marked  by  the  X.) 


10.     (Chant) 


I 


Iii  a. 


In  e. 


m 


InC- 


-In  a. 


11. 


F-  i    F- 


InBb- 


-lu  F- 


In 


12.     Close. 

>  LL    W  .         X  X 

$SH         -J— J— U- 


In  Bb. 


x     x 


13. 


XXX 


14. 


Open.  Close. 

XXX 


-4   . 


15. 


i 


II 


150 


HARMONY 


16.    ( Chant ) 


$&==PJ=£Ef=3=rr^^^^      | 


fj^=i-. 


££ 


fzzf=zp=p=q 
-* 


IncJ- 


-In  B 


In  08. 


18.     ( Hyiun-Uiiie) 


=4=1 


Ind- 
x 


-In 


-In  g. 


19.     (  Hymii-tune ) 
x 


&£ 


I 11~ 


In  e In  G 


— In  a. 

x 

*  '    P  •    •  .  I  » — •    P       IN    += 

^Sl^^l 


-In 


20. 


r-n  o — • — 

^        S  V      I    — t^ 


In  e — 


HARMONY 


151 


tr 


In  D 


In  A 


-lud— 


In  A In  I 


-In  D. 


II 


BASS   MELODIES   TO    BE    HARMONIZED 
(Introduce  inversions  of  secondary  7ths  in  each  exercise.) 

21. 


g       p    =f a — F0—        —  ^— !- 

k=C  EE   E 


In  G.- 


II 


*    * 


22. 


23. 


24. 


H 

3 

25.  ____^  ^ 


26. 


152 

27. 

HARMONY 

• 

^    \     r* 

• 

\        J 

J 

J   n. 

J 

9 

: 

J 

*  • 

0 

II 


28. 


\  ^  b    1                          *        w        i 

*        J 

W 

•           1 

7    4-    '           •  •        • 

3           ^ 

1                p»_ 

t 

1  rv    u                                                                 1          ^ 

i     4          -Ji   i 

II 

*1«,P     ^         & 

J      » 

_g 

M 

\  --S  b       r                  •               W             •  •    * 

^                                    *               • 

&       II 

1           '                                  • 
29. 

•^                    1      1 

f~\  •      h     ,      O                                                              | 

\      P      f2 

^?  •        1 

•1..P   h»>        |          ,     ~<A      J  J 

r      •             «     ' 

2       If 

¥ 
i 

-^     tl   K^d                     '     .  .             ~-  9       s~* 

r  -fi'     • 

III 


CHAPTER  XXXIV 


CHORDS    OF   THE    NINTH 


154.  WE  have  now  discussed  the  chords  most  used,  and  the  student  is  advised  to  review 
the  preceding  chapters.  It  will  be  well  to  write  on  four  staves,  and  to  transpose  some  of  the 
exercises,  introducing  passing  tones  (both  accented  and  unaccented)  and  auxiliary  tones  in 
moderation.  It  is  also  recommended  that  a  beginning  be  made  in  the  use  of  the  C  clefs  (alto 
and  tenor).1  THE  STUDENT  is  NOW  READY  FOK  INVESTIGATION  ON  HIS  OWN  ACCOUNT,  IN  LOOK- 
ING UP  INSTANCES  OF  THE  EMPLOYMENT  OF  VARIOUS  CHORDS  AND  CHORD  SUCCESSIONS',  the 

works  of  the  masters  from  Bach  to  Schumann  exist  in  editions  so  inexpensive  that  it  is  easy 
to  form  gradually  an  adequate  collection  of  them,  and  not  only  to  become  acquainted  with 
the  best  literature,  but  to  gain  a  living  sense  of  harmonic  questions  as  they  present  themselves 
in  the  music  of  the  great  composers. 

1  The  C  clef  has  been  used  for  all  the  voices  except  the  bass,  and  is  still  much  employed 
in  orchestral  music  (for  the  viola,  violoncello,  bassoon,  trombones,  etc.).  On  whichever  line 


of  the  staff  it  Is  employed,  it  designates  the  tone 


alto 


i~*~:  and  tenor 


are  consequently  the  same  as  [fli) .  and  ["^' . 


HARMONY 


153 


will  appear  as  follows,  when  written  with  these  clefs. 


155.  Before  entering  upon  the  subject  of  this  chapter,  we  must  under- 
stand the  fundamental  idea  of  the  suspension  and  the  appoggiatura. 

When  any  tone  of  a  chord  is  delayed  in  moving  to  that  tone  of  the 
following  chord  to  which  it  would  naturally  proceed,  by  being  prolonged 
into  the  following  chord  (of  which  it  does  not  form  a  harmonic  part),  a 
dissonance  is  produced  requiring  a  resolution.  The  tone  referred  to  of  the 
first  chord  is  then  said  to  be  SUSPENDED,  and  is  regularly  resolved  by  later 
proceeding  upward  or  downward  to  its  proper  tone  in  the  second  chord. 

k — ^  i  t i^-^  !  I 

^TJ       J— H-*=F^ &— H~< 


P 


- 


156.  An  APPOGGIATURA  is  a  tone  not  suspended,  foreign  to  the  chord 
with  which  it  occurs;  in  other  words  it  is  a  tone  dissonant  from  the  chord, 
and  must  move  diatonically  downward  or  upward  in  its  resolution. 


Suspensioa 


Double  appoggiatura 
X 


Passing  and  auxiliary  tones  have  been  defined  ( §  §  103,  104.  147). 

THE   CHORD   OF   THE    NINTH 

157.  This  chord  is  formed  by  adding  another  3d  to  a  chord  of  the  7th, 
just  as  we  formed  the  chord  of  the  7th  by  adding  another  3d  to  the  triad. 
It  clearly  is  possible  to  construct  seven  such  chords  in  every  major  and 
minor  key,  but  many  of  them  have  no  harmonic  consequence;  most  of  those 
which  are  available  enter  by  means  of  suspensions,  appoggiaturas,  and 
passing  or  auxiliary  tones. 


154 


HARMONY 


158.  The  dominant  chord  of  the  9th  is  the  one  chiefly  employed,  and 
properly  used  is  productive  of  admirable  results.  Our  attention  will  there- 
fore be  chiefly  directed  to  it,  before  we  consider  chords  of  the  9th  on  other 
degrees  of  the  scale.  It  occurs  in  major  keys'  (in  which  the  9th  is  usually 
major,  though  occasionally  chromatically  altered  to  a  minor  one,  Ex.  2), 
and  in  minor  keys  (in  which  the  9th  is  usually  minor,  sometimes  being  chro- 
matically altered  to  a  major  one,  Ex.  4). 

2.    ,  x_ 


9th. 

159.  As  there  are  five  tones  in  this  chord,  we  must  omit  one  when 
but  four  voices  are  used;  no  tone  maybe  doubled.  The  root  and  9th  are  of 
course  always  present.  The  chord  loses  in  character  if  the  7th  is  absent, 
and  the  omitted  tone  is  therefore  usually  the  3d  or  5th ;  as  is  the  case  with 
the  chord  of  the  7th,  the  result  is  stronger  if  the  3d  (leading  tone)  be 
kept;  the  5th,  however,  is  occasionally  present,  to  the  exclusion  of  the 
3d,  especially  when  the  3d  appears  in  a  subsequent  chord,  and  we 
thereby  obtain  a  better  voice-leading. 
3. 


9th. 


4. 


9th. 


1  A  chord  of  the  dominant  9th,  standing  by  itself,  is  even  stronger  in  giving  a  feeling 
of  tonality  than  is  the  dominant  7th;  it  not  only  fixes  the  key  but  the  mode  (with  the  rare 
exceptions  caused  by  chromatic  changes,  as  mentioned  above).  It  is  an  interesting  fact 
that  this  chord  Is  really  a  combination  of  the  dominant  and  leading  tone  7th  chords. 


HARMONY 


155 


160.  The  9th  may  be  prolonged  from  a  preceding  chord,  or  may  enter 
by  step  or  by  skip,  not  needing  to  be  prepared;  its  customary  resolution  is  one 
degree  down,  the  root  ascending  to  the  tonic,  the  7th  descending  one  degree, 
the  3d  (if  present)  ascending  to  the  tonic,  and  the  5th  (if  present)  either  as- 
cending or  descending. 


9th. 


9th. 


9th. 


9th. 


9th. 


9th. 


In  another  common  resolution,  the  9th  descends  while  the  other  voices 
remain  stationary,  the  second  chord  thus  being  a  chord  of  the  dominant 

7th.1 

6.  x 


9th. 


The  9th  sometimes  proceeds  to  another  tone  (not  the  root)  of  the 
following  chord  of   the  7th,  and   may  also  be  followed   by  another   triad 
than  the  tonic  (Ex.  12). 
7. 


9th. 


9th. 


161.   The  9th  not  infrequently  resolves  upward. 

-K  1 

I    XCi  d 


9th. 


9th. 


1  Strictly  speaking,  the  rhord  of  the  Oth 
4  rxml  8  (a)  and  (6)  );  the  interval  of  the  Oth  <1<> 
inullv  'hroiiKh  the  dominant  7th  chord. 


lixM  not  rp^olvc  in  this  and  similar  rn***  (Fi. 
resulvc,  but  thr  chortl-fMolution  takes  place 


156 


HARMONY 


9th. 


Instead  of  resolving  upward  to  the  3d  of  the  chord,  it  may  descend  to  that 
tone  an  octave  lower,  making  a  skip  of  a  7th  ; 
9.    x 


or  may  leap  to  another  tone  of  the  same  harmony. 
10.  x      x 


9th.    9th. 

In  the  following  it  is  used  as  a  passing  tone,  in  an  ascending  and  a 
descending  passage. 

X  N       I  X 


r-*- 

Finally,  the  9th  may  be  irregularly  prolonged  into  the  next  (different) 
chord;  see  Ex.  7. 

12.x        * 


9th. 


Observe  in  Ex.  2  the  minor  9th  in  a  major  key,  entering  by  preparation ;  in  Ex.  4  the 
major  9th  in  a  minor  key,  entering  by  skip;  in  Ex.  3,  8  (a)  the  omitted  3d,  which  is  given  us 
in  the  chord  of  resolution;  in  Ex.  5  (a)  (6)  the  different  resolutions  of  the  5th  in  order  to  avoid 
consecutive  5ths;  that  in  Ex.  4,  8  (a)  it  may  be  properly  considered  an  appoggiatura,  and  in 
11  as  a  passing  tone;  that  in  Exs.  2,  3,  6,  8  (6)  it  is  suspended;  that  in  7.  9,  10  it  moves  in 
some  cases  by  a  skip.  (Cf.  §16-').) 


HARMONY 


157 


NOTE.  Something  should  be  said  here  concerning  a  view  held  by  many  theorists,  espe- 
cially in  England  and  France.  It  is  briefly  this,  that  chords  of  the  leading-tone  7th  in  major 
and  minor  are  to  be  regarded  as  chords  of  the  9th  with  the  root  (or  "generator")  omitted, 
and  that  the  first  inversion  of  the  leading-tone  triad  is  a  dominant  7th  chord  with  its  root 
omitted. 


This  opens  an  interesting  field  for  speculation,  and  is  to  a  certain  extent  justified  by  facts 
in  acoustics,  but  hardly  important  to  the  student  who  is  learning  about  chords  and  their  uses. 
From  a  musical  point  of  view,  the  value  of  this  theory  seems  questionable  when  one  considers 
that  the  tone  F  of  the  following  chord  of  the  6th  will  nearly  always  ascend,  and  may  even  be 
doubled  (in  which  latter  case  one  F  will  ascend),  neither  of  which  things  is  true  of  the  7th  in 
the  7th  chord  of  which  this  chord  of  the  6th  is  supposed  to  be  a  part. 


It  is  a  fact  that  if  the  tones 


and  then  the  low 


Q    be  played  and  sustained, 
II 


be  sounded,  we  almost  feel  as  if  the  first  chord  were  com- 


pleted by  the  additional  tone;  but  this  is  rather  of  acoustic  than  harmonic  interest. 

162.  It  is  most  often  the  case  that  the  9th  is  placed  in  the  soprano; 
it  may,  however,  be  in  either  alto  or  tenor.  The  only  thing  absolutely 
necessary  is  that  in  pure  four-part  writing  the  $th  shall  always  appear  above 
the  root  and  be  distant  at  least  a  9th  from  it,  for  the  result  otherwise  will  be 
excessively  harsh. 

Possible  in  instrumental  music.        All  good. 


Oth  in  alto. 


Oth  in  tenor. 


The  above  are  all  good  in  minor  keys  also. 


158 


HARMONY 


A  fine  example  of  the  9th  in  the  alto,  with  the  3d  above  it,  is  seen  in  the  extract  from 
the  "Meistersinger"  overture  (§  147). 


9th. 

163.   Some  examples  of  this  chord  follow,  illustrating  various  points 
of  entrance  and  of  resolution. 

WAGNER:  "Lohengrin" 


SCHUBERT:  Sonata,  Op.  42 
9th.. 


DEBUSSY:  "La  Demoiselle  felue1 
L 


Hh. 


BEETHOVEN:  C  minor  Concerto 


9th. 


BEETHOVEN:  Sonata,  Op.  53 


9th. 


HARMONY 


159 


WAGNEB:  "Das  Rheingold  " 


SCHUMAXK:  "Genoveva"  Overture 


9th. 


SCHUBEBT:  Unfinished  Symphony 

I. 


9th. 


8va. 


Mrs.  H.  H.  A.  BEACH:  "Fireflies" 


'"r--1 

-•-b* —  ««-  " 


9th. 
WAGNER:  "Die  Walkttre" 


9th. 


c=»     '        •* 
*&.    '   <=>•       -|< 
J=r        I     <^    *i 


^3 

9th. 


WACXKK:   "  Parsifal ' 


160 


HARMONY 

CHADWICK:  "  Lovely  Rosabelle' 


9th. 
CHOPIN:  Bb  minor  Sonata 


MENDELSSOHN:  Chorale 


9th. 


SCHUMANN:  Toccata 


In  these  last  three  examples  the  9th  appears  in  an  authentic  cadence.  We  now  have 
an  illustration  of  successive  chords  of  the  9th,  as  well  as  one  of  successive  chords  of  the  7th. 
It  is  but  fair  to  say  that  they  are  to  be  regarded  as  specimens  of  an  exceedingly  free  treatment 
of  these  chords;  the  question  of  pure  part-writing  does  not  enter.  The  extract  from  Debussy 
is  from  an  opera,  and  in  music  for  the  stage  far  greater  liberty  is  allowable  than  with  what  is 
called  absolute  music:  the  same  is  true  about  the  piano  piece  of  Grieg. 

DEBCSSY:  "Pelleas  et  M^lisande" 

EHE 


HARMONY 
GRIEG:  Nocturne,  Op.  54,  No.  4 


161 


INVERSIONS   OF   THE    CHORD    OF   THE    DOMINANT   NINTH 


164.   There  are  four  inversions, 
(£ 


of  which  (a)  and  (c)  are  very  useful,  (6)  being  available  when  resulting 
naturally  from  the  voice-leading,  but  the  last  inversion  not  worth  consid- 
eration, on  account  of  its  harshness  (  §  162) . 

CHORDS  OF  THE  NINTH  ON  OTHER  DEGREES 

165.  We  have  seen  that  the  chord  of  the  dominant  9th  may  enter 
by  preparation,  by  step,  or  by  skip;  that  it  may  be  resolved  by  prolonga- 
tion into  the  next  chord,  by  descending,  or  by  ascending.  This  is  largely 
the  case  with  9th  chords  on  other  degrees  of  the  scale.  These  nearly 
always  appear  as  suspensions,  appoggiaturas,  passing-tones  or  auxiliary 
tones,  but  their  treatment  is  more  restricted ;  the  chord  of  the  dominant 
9th  resembles  that  of  the  dominant  7th  in  its  resolution,  but  such  is  not 
necessarily  the  case  with  other  chords  of  the  9th.  It  should  also  be  mid 
that,  as  the  interval  of  the  9th  really  forms  an  integral  part  of  the  chord,  the 
requirements  of  the  definition  of  the  term  suspension  are  not  met  (§  S<>?) ;  it  i* 
more  logical  to  my  that  the  9th  w  prepare,!,  ax  7ths  are  prewired  (p.  l.U).  and 
to  consider  that  lee  do  not  have  a  true  suspension. 

The  following  examples  an-  given  to  show  li«>w  these  chords  of  the  9th 
apl>ear  (")  through  susi>ension,  (//)  as  apiM.ggiaturas,  (<•)  as  passing-tones. 
(</)  as  auxiliary  tones. 


etc. 


162 


HARMONY 


4- 1- 


(c) 


9       9  r 

±=&g= 


«*) 


8     9 


8         9 


In  (a)  the  9th  may  also  resolve  upward,  or  move  downward  by  skip ;  in  (c)  it  may  be 
prolonged  into  the  next  chord. 


(a) 


J I 


IH 

^ «*y— 


etc. 

I 


A_A 


r    i 


J 


0  I      ,  ,    I      i      i 


J    J.     J. 


8       9 

The  chord  of  the  9th  on  the  super-tonic  is  often  used  in  a  cadence  as  follows,  and  occa- 
sionally with  the  chromatic  change  indicated  in  (/),  in  which  latter  case  it  becomes  a  domi- 
nant 9th  derived  from  the  dominant  key. 


(O 


9th. 


HARMONY 


163 


BACH:  Preludio  con  fuga.  (Peters  Ed.  No.  207) 
^  -d=  =-l  -i— J J— u 


9th. 
BACH:  Well-Tempered  Clavichord,  Vol.  I,  22d  Fugue 


9th. 
HENSCHKL  :  "Requiem" 


SE 


Bftfr-fl =§=£-!  iU&^i'' 


166.  The  secondary  chords  of  the  9th  are  flexible  in  treatment,  although  great  care 
must  be  taken  that  the  leading  of  the  voices  is  pure  and  musical;  the  inherent  harshness  of 
many  of  these  chorda  is  softened  by  the  manner  in  which  they  are  introduced,  as  indicated 
above.  It  thould  be  observed  that  the  occurrence  of  the  interval  of  a  9th  does  not  of  itself  indicate 
a  reed  chord  of  the  9th.  In  the  following  the  note  G  is  a  simple  appoggiatura  in  one  voice,  and 
the  chord  is  really  a  chord  of  the  6th. 

X 


CHAPTER  XXXV 

ff 

EXERCISES   WITH    CHORDS   OF   THE    NINTH 


167. 
1. 


96       7 
7 


6         6 
6         4 


9    6 


164 


HARMONY" 


2. 


3  39  6 

75 


35  96 

4  7 

3 


67 


Open • 


f       5i     9f    8     6      f   4     6          6         9 

726 
4 


6         87 
4         |- 


"1.   fl                          m 

o          P 

EZ 

i^"        4*^ 

F—            P           1* 

-S  A    1          r 

[       r 

i 

P"'^       4t^ 

1              I 

*»•              i. 

1 

IJ 

3                     967                     6967$            67 

7                                                7             g                         4 
f-      -                       .3 

5. 


g^i^^-rr1^^ 


967          6 
7  4 

3 


Open- 


-Close. 


56  9  7966 

7  7 

3  3 


6  676 

4 


7. 


t 

1* 

r       r       « 

N          ! 

~^  4~** 

'       • 

r     fS         1 

56979               269                   6 
77                                      6 
33                                    3 

79 
76      7 
3 

^=F=fe 


6966 
7  , 


9. 


Adagio 


_^  -i 

;           TI 

H  h— 

j  r    r 

,g>. 

-^-4  '  1  — 

-1  1  1 

—  v— 

^    II 

6937                    4 
5                                 3 
,      3 

967                              4 
7                                           3 
3 

HARMONY 


165 


10. 


Allegretto 


346 
3 
2 


967 

7 

3 


6967 
7 
3 


11. 


Moderate 


Open- 


-Close. 


{?  |  


9  726  6 987 

5  4 3 


6  6  98.7 

65  X 


4 
35 


Chords  of  the  9th  are  indicated  by  a  x ;  in  some  exercises  ( e.  g.  Xo.  12  ) 
the  7th  is  to  be  omitted. 


12.         Open- 


•Close- 


~  y  i  fr~~         ,>j  i  ^        i         "1T>3     i  i  ^-s     I  i  1 1*  •  I  r  "j      I   L     n 
^B^^^fJ^g^fMJlgSpEJE^H 


In  ST. 
13.         Close. 


V 


^ 


14. 


""II 


In  a.  In  C 


16. 


gjgg 


•       ^ 


|] 


16. 


!=s= 


>       r 


17.  x 

j_,_4-4- 


5— -fziE=^— n 

^z^E: 


166 


HARMONY 


18.  Close.  Open.- 


-Close. 


^TTFH  4f» rrN'rr^^fl 

i   '  i '   i     ..'  i '   i   i  f  r  i  '  T  T  rfl 


19.  Open 

Larqhetto.    x  x 


-Close- 


-Open. 


irgl 


fi^    ^S^3 


II 


In  G. 


In  e. 


InG. 


^ 


II 


In/. 


In  Afc 


CHAPTER  XXXVI 

CHORDS    OF   THE    ELEVENTH    AND   THIRTEENTH 

168.  No  one  can  say  what  will  be  the  future  of  music  on  the  harmonic 
side;  judging  from  the  past  there  will  be  further  development,  at  least  in 
the  direction  of  greater  freedom  in  the  use  of  chords.  In  the  history  of 
music  we  find  at  different  periods  the  ecclesiastical  modes  giving  way  to 
our  present  scale  system,  the  mediaeval  vagueness  of  tonality  abandoned 
for  our  modern  definite  feeling,  and  a  purely  contrapuntal  way  of  working 
developed,  by  the  growth  of  harmonic  understanding,  into  the  methods 
employed  in  the  master  works  of  Bach.  We  know  approximately  when 
the  use  of  suspensions  became  common,  when  the  dominant  7th  was  allowed 
to  appear  without  preparation,  when  the  authentic  cadence  came  into 
ordinary  use.  During  the  last  century  freedom  has  been  gained  in  the  use 
of  secondary  7ths  without  preparation,  in  the  introduction  of  chromatic 
passing-tones,  etc.,  and  of  chromatically  changed  chords,  and  in  the  manner 


HARMONY 


167 


:>f  regarding  the  tritone  and  the  cross  relation;  the  chord  of  the  9th  has  been 
granted  its  place,  as  an  independent  factor,  in  the  family  of  chords.  In- 
vestigation and  experiment  are  still  going  on. 

169.  With  the  chords  of  the  llth  and  13th,  however,  we  seem  to  have 
some  to  the  end  of  independent  chords.  From  our  present  point  of  view 
they  appear  to  exist  mainly  through  suspension,  or  by  means  of  appoggia- 
turas,  and  passing  and  auxiliary  tones.  But,  although  a  discussion  of  them 
might  be  left  until  later,  in  the  chapters  on  suspension,  etc.,  it  seems  pref- 
erable to  make  a  brief  statement  here  as  regards  their  use. 


CHORD   OF   THE    ELEVENTH 

170.  In  the  same  way  that  we  get  the  chord  of  the  9th  by  the  addition 
of  a  3d  to  the  chord  of  the  7th,  so  we  obtain  tne  chord  of  the  llth  by  add- 
ing another  3d  to  the  chord  of  the  9th.  A  chord  of  the  llth  can  theoreti- 
cally be  erected  on  any  tone  of  a  major  or  minor  scale;  but,  as  is  the  case 
with  the  chord  of  the  9th,  the  chord  of  the  llth  with  the  dominant  for  its 
root  is  the  one  most  employed. 

7th.     9th.     llth. 


Observe  that  in  the  examples  given,  the  chord  enters  in  the  manner  de- 
scribed in  §  169. 

171.  It  is  clear  that  two  of  these  six  tones  must  be  omitted  in  four- 
part  writing;  that  the  llth  is  merely  the  4th  placed  an  octave  higher:  and 
that  it  will  consequently  often  appear  as  a  suspension  (the  4th  being  re- 
garded in  suspensions  as  a  dissonant  tone  that  must  be  resolved) ;  examples 
of  this  (a),  as  well  as  of  the  llth  entering  as  an  appoggiatura  (b),  and  passing 
(c)  and  auxiliary  tone  (d)  follow.  The  llth  is  resolved  either  downward 
or  upward. 


168 


HARMONY 


In  the  following  example  of  this  chord,  with  an  unusual  resolution,  we  see  how  easy  it  is 
for  theorists  to  differ;  for  it  is  also  quite  naturally  explained  as  being  a  chord  of  the  dominant 
7th,  placed  below  an  inverted  pedal  (the  tone  D  of  the  soprano;  cf.  the  chapter  on  the  Pedal). 

SCHUMANN:  Novellette,  Op.  21,  No.  8 
X 


172.  It  may  also  occur  together  with  a  suspension  of  another  voice] 
as  the  llth  is  the  same  tone  as  the  4th  (an  octave  higher),  the  3d  is  of 
course  omitted  in  the  dissonant  chord,  and  we  must  choose  whether  the 
5th,  7th,  or  9th  is  to  be  also  omitted. 

x  xx 


f 


5th  omitted. 


r 


-J       J- 


7th  omitted. 


r    r    r 

9th  omitted. 


J- 


"WAGNER:  "  Tristan  und  Isolde" 
X 


llth. 

MENDELSSOHK:  Chorut,  "  For  all  the  Gentiles  "  ("  St  Paul ") 

J     .J       J U 


llth. 


HARMONY 


169 


MENDELSSOHN:  "Midsummer  JCiglit's  Dream"  Overture 

_4_J_J_  JL_ 


r 


r 


llth. 


CHORD    OP   THE    THIRTEENTH 


173.   By  adding  yet  another  3d  to  the  chord  of  the  llth,  we  obtain 

the  chord  of  the  13th. 

7th.     9th.     llth.     13th. 


The  addition  of  another  3d  to  the  chord  of  the  13th  brings  us  to  the  tone  two  octaves 
above  the  root,  and  therefore  to  the  end  of  all  possible  chords,  as  we  should  then  begin  our 
series  of  3ds  over  again. 

174.  This  chord  also  usually  appears  with  the  dominant  for  its  root, 
and  is  logically  explained  as  resulting  from  a  suspension,  an  appoggiatura. 
a  passing  tone  or  an  auxiliary  tone. 

In  four-part  writing  three  of  the  seven  tones  of  this  chord  must  be 
omitted.  A  few  examples  are  given  of  its  most  common  use. 

13th.  13th. 


BEETHOVEN:  9th  Symphony 
^ ^x 

Ea  3-  _u  — -^f—  -f-   fj 


170 


HARMONY 


:  "Der  fliegende  Hollander" 
X 


13thT 


:  Qnintet  from 
4  Die  Meistersiuger  " 
X 


BRAHMS:  Intermezzo,  op.  119. 


13th. 


WAGNEK:  "Die  Meistersinger"  (p.  389)] 
X 


13th  (complete) 

GHIEO:  Song,  "Ein  Schwan* 


A 

etc.        < 


•3.*!; 


ET* 

13th. 


13th. 


DEBUSSY:  "Pellet  et  Melisande" 
X 


9th.    13th.  9th. 

In  the  last  example  we  have  this  chord  used  independently;  a  rare  instance.  It  is  given 
rather  to  show  that  experiments  are  being  made  in  this  direction;  the  result  may  tend  to 
further  emancipation  of  the  chord  of  the  13th. 

SCHUMANN:  "Des  Abends,"  Op.  12,  No.  1. 

J*    .  I"     J     A. 


X  9th. 13th. 7th. 

(As  this  is  for  pianoforte,  and  the  pedal  sustains  the  other  tones  of  the  dominant  har- 
mony, the  chord  may  be  regarded  as  a  true  13th. > 


HARMONY 


171 


CHAPTER  XXXVII 

CHROMATICALLY   ALTERED    CHORDS 

176.  So  far  we  have  been  dealing  with  chords  of  a  definite  tonality, 
which  were  classified  mainly  as  triads  and  seventh  chords  (in  either  funda- 
mental or  inverted  position)  on  the  various  degrees  of  the  major  or  the 
minor  scale.  We  must  now  enlarge  our  harmonic  vocabulary  by  studying 
an  important  group  of  chords  which  are  formed  by  chromatic  alteration. 
The  principle  is  this,  that,  whenever  any  voice  progresses  by  a  whole  tone, 
the  latter  may  be  subdivided  into  semitones  by  the  introduction  of  appro- 
priate accidentals,  e.g. 

'         4- 


176.  Theoretically,  any  factor  of  a  triad,  or  of  a  7th  or  of  a  9th  chord 
may  be  chromatically  raised  or  lowered.     Some  of  these  formations  will 
not  differ  from  chords  found  in  a  regular  scale-series;  some  are  used  but 
rarely,  and   as  passing  chords;   while   others  are  so   frequent   in  inverted 
positions  that  they  are  felt  to  have  a  definite  identity  and  have  received 
appropriate  names. 

177.  The  3d  of  triads  is  the  factor  which  decides  whether  the  mode  be 
major  or  minor;  either  the  root  or  the  5th  may  be  chromatically  altered, 
but  those  chords  which  arise  from  an  alteration  of  the  5th  are  decidedly  of 
the  most  importance,  e.g. 

(1)         (2)          (3)         (4)         (5)         (6)         (7) 


In  (1)  we  have  a  major  triad  with  nn  augmented  5th.  As  this  is  an  alteration  of  f-E-G. 
it  may  be  used  as  a  passing  chord  in  C  major,  I"  major,  <i  major,  or  e  minor;  t.  «.  in  keys  in 
which  C-E-Ci  is  tonic,  dominant,  subdominant,  or  tmbmediant  triad,  e.g. 

C  Major 


172 


HARMONY 


F  Major. 


G  Major. 


e  Minor. 


' 


£:s^ 


J 


J.       J.       J.      J       J 


^f^ 


This  triad  C-E-GJ  is  also  found  in  a  minor,  in  that  case  being  not  an  altered  chord,  but 
the  regular  augmented  triad  on  the  third  degree;  and  in  that  relationship  its  use,  &s  we  have 
seen  (§  61),  is  comparatively  rare.  Henceforth  it  will  often  occur  as  an  altered  chord. 

Of  (2),  a  minor  triad  with  an  augmented  5th,  an  example  will  soon  be  given  (p.  175). 
Although  (3)  is  classified  as  a  diminished  triad,  it  also  occurs  very  frequently  as  a  major  triad 
with  an  augmented  root,  used  as  a  passing  tone;  e.g. 


(4)  A  triad  with  a  diminished  5th  and  a  diminished  3d  is  comparatively  rare  in  its  funda- 
mental position  (except  as  a  passing  chord),  but  in  its  first  inversion  is  one  of  the  most  useful 
chromatic  harmonies, —  the  chord  of  the  augmented  tirtk;  e.g. 


(5)  A  triad  with  a  diminished  5th  and  a  major  3d  is  sometimes  found  in  the  first  inversion  ae 
a  passing  chord  with  striking  effect;  e.g. 

CHERUBINI:  Requiem  for  Men's  Voices 

' 


I. —*r-     •  -  t» g^1  •  —  '    M^        i  *»-— <f»'     r"Q 

-jgjflTb,      ^Tf=>-  i,fg- 
_-^^t>4  t"  t    >^->'*  •  h-z 

X  I 

(6)  A  minor  triad  with  a  lowered  5th  is  very  common ;  e.g. 


r    ' 


HARMONY 

(7)  is  sometimes  found  as  a  passing  chord;  e.g. 


173 


r 


178.    Triads  with  an  augmented  5th  are  also  practicable  when  inverted,  i.e.,  as  6  and 
6-4  chords;  e.g. 

C  Major.  F  Major. 


179.    In  like  manner  with  7th  and  9th  chords  —  although  theoretically  any  factor  may  be 
altered,  the  5th  is  most  frequently  so  changed;  e.g. 


(«)         (»)        (c)         <<*) 


In  this  table  we  have  some  of  the  most  usual  chromatically  altered  7th  and  9th  chords. 
Certain  of  these  combinations  are  more  common  in  inversions,  and  they  are  generally  used 
in  open  position;  for  if  the  altered  5th  and  the  7th  are  near  together  the  effect  is  usually  harsh. 
(a)  is  a  dominant  7th  chord  with  augmented  5th;  as  a  4-3  chord  with  the  augmented  tone 
in  the  bass  it  is  rare,  but  all  the  other  positions  are  common  and  extremely  effective.  Ob- 
serve that  by  the  use  of  open  position  the  7th  and  the  altered  5th  are  kept  apart;  e.g. 


C  rare  ) 


- _. _ — M     •    r-- — n — *^ r  — 


(h)  is  extremely  rare  in  fundamental  position,  but,  as  a  6-5  chord,   is  by  no  means  uncom- 
mon, and  as  a  4-3  chord  is  of  great  importance;  e.g. 

BA<  II :  St.  Matthew  Passion 
X 


(c)  r.  diminished  7th  chord  with  lowered  3d,  is  often  found  in  fundamental  position,  and  by 
reason  of  the  diminished  3d,  caused  by  the  chromatic  alteration,  is  one  of  the  most  expres- 
sive chords  in  music;  e.g. 


174 


HARMONY 


BACH:  Mass  in  B  minor 


MENDELSSOHN:  "Hear  My  Prayer" 
X 


ay»  n 

S'    c 
— n  z 


1 .    *    T          r  £   f  • 
j^-4-1  J.  j_j^  '  i 

T"T"T       r*     i  *r^   '"      U 


This  chord  (c)  in  its  first  inversion,  where  the  diminished  3d  becomes  an  augmented 
6th.  is  most  important,  and  will  be  fully  treated  later;  e.g. 


is  often  used  as  a  passing  chord;  e.g. 


.  6 
5 


(O  and  (/),  dominant  major  and  minor  9th  chords  with  augmented  5ths,  are  very  common:  a 
beautiful  example  is  given  from  Wagner. 

"  Das  Kheingold  " 
X  X 

I 


A 


- 


, 
-•^  \  a,>    i3 

•      3E&^        U 


The  second  theme  in  the  first  movement  of  Beethoven's  Heroic  Symphony  affords  a  re- 
markable illustration  of  several  chromatically  altered  chords. 


HARMONY 


175 


to:g— S^^tog^          r^=z: 

E^^qK- i         dE=zdBE:r 


Sl^iS 


At  (a)  we  have  a  major  triad  with  augmented  5th;  at  (6)  a  secondary  7th  chord  with 
augmented  5th;  at  (c)  a  minor  triad  with  augmented  5th,  and  at  (d)  an  inverted  dominant 
7th  with  augmented  root. 

180.  Although  in  many  cases  (as  in  the  examples  given  above)  these  altered  tones 
proceed  by  a  semitone,  this  is  not  invariably  necessary.  They  may  enter  by  a  leap,  especially 
in  instrumental  music;  e.g. 


~r  i       •<*•     -£>-      «j     i 


SCHUMANN:  Song, "  Sttsser  Freund."    (Op.  42) 

X 


181.  As  to  the  progression  of  the-m  altered  tones  —  when  augmented  they  generally 
continue  to  ascend,  and  when  diminished  to  descend.  This  is  illustrated  in  all  the  exnmpl«-p 
above. 

Chromatic  alterations  are  often  written  enharmonically,  partly  to  wcuro  nimplirity  in 
writing  and  also  to  conform  to  the  conventional  notation  of  the  chromatic  wale,  in  which 
the  seventh  degree  remains  lowered  and  the  fourth  decree  raised,  in  both  awcr-mling  and  d«»- 
scending  passages;  e.g. 


176 


HARMONY 


182.  Two  very  important  chords  in  music  are  those  derived  from 
chromatic  alterations  of  the  triad  on  the  second  degree  in  the  minor  mode. 
This  triad,  with  its  diminished  5th,  is  a  somewhat  unsatisfactory  dissonance, 
as  we  have  seen  (§  §  68,  60) .  Early  in  the  development  of  music,  we  find 
composers  altering  it  into  one  with  a  perfect  5th  by  lowering  the  root;  e.g. 
in  c  minor. 

Instead  of 


The  customary  resolution  is  either  to  dominant  or  tonic,  and  in  order 
to  avoid  unmelodic  skips  and  the  possibility  of  consecutive  oths  and  8ves, 
the  triad  is  generally  inverted  and  used  as  a  chord  of  the  6th.  This  triad 
on  the  second  degree  of  the  minor  mode  with  a  lowered  root,  when  in  the 
first  inversion,  is  known  as  the  Neapolitan  Sixth. 


Good. 


183.  This  altered  triad  is  by  no  means  limited  to  the  first  inversion; 
in  instrumental  music,  especially,  it  is  often  found  in  the  fundamental 
position,  or  even  as  a  6-4  chord,  e.g. 

CHOPIN:  Prelude  No.  20 


3= 


HARMONY 


17' 


VON  WEBER:  Overture  to  "Der  Freischiitz" 
X 


184.  This  triad  on  the  second  degree  in  the  minor  mode  is  often  al- 
tered, by  allowing  the  root  to  remain  as  in  the  key  and  raising  both  the  3d 
and  the  5th  a  semitone,  e.g. 

is  changed  into 


We  often  find  phrases  like  the  following. 

x  OB 

-teh-J— 


$ 


&S 


_"<' 


I 


l 


1 

J  J  J 


55    7    r 

$ 


In  the  next  passage,  from  Beethoven,  we  find  both  of  these  chromatically 
altered  chords  from  the  second  degree  used  in  succession. 


Sonata,  Op.  31,  No.  2 
X X 


186.   The  Neapolitan  Sixth,  although  derived  from  the  minor  mode, 
is  often  found  in  the  tonic  major;  here  is  one  characteristic  example. 


BKAIIMS:  "Deutsches  Requiem" 
X.          x  X 

: 


186.    The  above  list  of  chromatically  altered  chords  is  not  complete;  hut  for  the  present 
it  is  sufficient  for  the  student  to  know  the  more  important  facts  as  Mated  above.      Little  by 


178 


HARMONY 


little  it  is  possible,  through  harmonic  analysis  and  the  study  of  modern  compositions,  to  become 
familiar  with  varied  effects,  which  can  be  explained  only  by  a  broad  application  of  these 
principles. 

In  modern  music  passages  like  the  following  are  of  frequent  occurrence,  the  free  altera- 
tions in  the  chorda  being  evident.    The  bass  is  a  tonic  pedal-point  (cf.  chapter  on  the  Pedal.) 


187.   The  following  melody  is  to  be  harmonized  with  the  aid  of  altered  chords. 


I^et  the  student  first  play  and  sing  this  melody,  then  harmonize  it,  and  finally  compare  with 
the  following  version. 


At  (a)  we  have  a  secondary  7th  chord  with  a  raised  5th;  at  (6)  a  third  inversion  of  a 
secondary  7th  with  a  lowered  5th;  at  (c)  a  dominant  7th  with  a  raised  5th,  and  at  (d)  a  simple 
triad  treated  in  like  manner. 

The  following  interesting  passage  from  a  modern  symphony  shows  the  dominant  7th 
chord  with  the  5th  raised  and  lowered  in  the  same  chord  in  different  voices. 


TSCHAIKOWSKI:  6th  Symphony,  (2<1  movement) 


HARMONY 


179 


"The  essential  fundamental  chords  are  but  few,  and  must  remain  so,  but  the  combina- 
tions which  can  be  made  to  represent  them  on  the  polyphonic  principle  are  almost  infinite. 
By  the  use  of  chromatic  passing  and  preliminary  notes,  by  retardations,  and  by  simple  chro- 
matic alterations  of  the  notes  of  chords  according  to  their  melodic  significance,  combinations 
are  arrived  at  such  as  puzzled  and  do  puzzle  theorists  who  regard  harmony  as  so  many  un- 
changeable lumps  of  chords  which  cannot  be  admitted  in  music  unless  a  fundamental  bass  can 
be  found  for  them.  Thus  the  chord  of  the  augmented  6th  is  probably  nothing  more  than  the 
modification  of  a  melodic  progression  of  one  or  two  parts  at  the  point  where  naturally  they 
would  be  either  a  major  or  minor  6th  from  one  another,  the  downward  tendency  of  the  ore 
and  the  upward  tendency  of  the  other  causing  them  to  be  respectively  flattened  and  shar- 
pened to  make  them  approach  nearer  to  the  notes  to  which  they  are  moving.  .  .  .  The  actual 
number  of  essential  chords  has  remained  the  same  as  it  was  when  Monteverde  indicated  the 
nature  of  the  dominant  7th  by  using  it  without  preparation,  unless  a  single  exception  be  made 
in  favor  of  the  chord  of  the  major  9th  and  its  sister  the  minor  9th,  both  of  which  Helmholtz 
acknowledges  may  be  taken  as  representatives  of  the  lower  note  or  root."  (From  the  article 
on  'Harmony'  by  Parry,  in  Grove's  'Dictionary  of  Music.') 


CHAPTER  XXXVIII 


188.    5,  5$  indicate  that  the  5th  is  first  a  diatonic  note,  and  in  the  next  chord  is  raised 
chromatically  (§  51.) 

1. 


T  i I 


55$  55$  55$  55$  55$  3766  2 

5$  5 


6—  677777777  6    52 


2. 


6  5  5f          6         f  67 


6  55$          76 

6  5 


3. 


4  _  — *— t-h=rt— 1  tz  -W* f  pz=4r±obi:  I J 


3*706  7 

25$  $          - 


ab 

3 


6  9 


180 


IIAHMONY 


I 


e    SB    75 

& 


5. 


I        6          7b 

4 

3 


&        6        7         7 

& 


5     5J 


f 


^ 


2        6 


II 


1 — h 


*        666        265$          $0797 


7. 


762  7,     6      6} 

5  3b   5      5 

30   


G      4 
5      3b 


7    6    6| 
b    5    4 

b    — 


,  ^ 


II 


885    6—  6       5584—     6 

5—  3b'2 

3  3J 


876     7b    6 

•S—        5b    4 


3b 


6JJ      6       367 
4 


8.     Grazioso. 


\»      m 


6R  3fl       7      t        35       Jf        32      2      4     2        6J     2        4         — 

4  59  3  4$  4          5 

3  3         — 


i 


6         —         7—76         —         7  26—7 

4          —          5    — 

3     i 

MELODIES   TO    BE    HARMONIZED 

CIn  No.  10  use  the  Neapolitan  6th  at  the  X;  in  No.  11,  use  the  different  alterations  of  11° 
at  the  points  marked  with  a  X:  cf.  §  §  182-184.) 

9. 


HARMONY 


181 


10. 


:3tzfc5bd 
pafc^gE 


t=t 


11. 


12. 


^=*=tf*= 


* 


i^E 


13.    Andante  con  molo. 


tr 


II 


5fe 


14.    Moderate  espresst'uo. 


, 


In  a. 


II 


In  e.  Iu  G. 


16. 


16. 


S      "      ' 
1^— 


s--  ^73 

.^ — s^J 


g 

«    5*     »      • 


E3EF^_t|^5 

— __±k___t=z_d 

g^B 


182 


HARMONY 


17.     Andante. 


NOTR.     In  Nos.  9-17  it  is  sometimes  the  case  that  there  are  to  be  chromatic  changes 
in  another  voice  besides  the  soprano. 

Bass  melodies  to  be  harmonized:  altered  chords  are  indicated  by  the  x,  and  passing  or 
auxiliary  tones  by  the  slur;  the  chromatically  altered  tone  may  appear  at  any  place  in  the 
measure. 

18.  v  v  v  v 


19. 


20. 


21. 


II 


CHAPTER  XXXIX 

AUGMENTED   CHORDS 


189.  WE  find  in  music  three  very  important  chords,  the  augmented 
6th,  the  augmented  6-4-3,  and  the  augmented  6-5-3.  In  each  of  these 
chords  the  characteristic  interval  is  the  augmented  Qth,  which  is  always  caused 


HARMONY 


183 


by  chromatic  alteration,  for  the  major  and  minor  scales  contain  .only  major 
and  minor  6ths.  The  interval  of  an  augmented  6th  may  be  formed  from  a 
major  6th  either  by  lowering  the  lower  tone  or  by  raising  the  upper  one,  e.g. 


Major  6th.  Aug.  6th.  Major  6th.  Aug.  Cth. 


and  from  a  minor  6th  by  altering  both  the  upper  and  the  lower  tone  at  the 
same  time,  e.g. 

Minor  6th.  Aug.  6th. 


I 


-;- 


190.  In  resolving  these  chords  the  general  tendency  is  for  the  voices  which 
contain  the  augmented  6th  to  continue  expanding  into  a  perfect  octave,  example 
(a) ;  occasionally  each  of  the  voices  descends  a  semitone,  as  at  (fc) ;  one  voice 
often  remains  stationary  while  the  other  moves,  (c)  and  (d) ',  sometimes  one 
voice  leaps  (e)  and  (/) ;  it  is  even  possible,  although  not  common,  for  both 
voices  to  converge  (#). 

(«)  (b)  (c)  (rf)  (e)  (/) 


These  resolutions  apply  to  all  of  the  three  augmented  6th  chords.  Each 
chord,  however,  has  special  points  of  treatment. 

191.    1st.  —  THE  AUGMENTED  6TH  CHORD. 

As  this  chord,  like  any  6th  chord,  consists  of  but  throe  different  tones, 
in  four-part  writing  the  question  of  doubling  has  to  be  settled.  As  both  of 
the  tones  forming  the  augmented  Gth  have  strong  tendencies  along  certain  lines, 
and  moreover  arc  very  characteristic  in  sound,  they  are  practically  never  doubled . 
it  iff  the  invariable  practice  to  double  the  ^d^.  counting  from  the  bass  of  the  aug- 
mented Ctth  chord.  The  usual  groupings  arc  as  follows: 


184 


In  free  pianoforte  writing  and  in  all  instrumental  music  with  more  than  four  parts,  these 
considerations  aa  to  doubling  do  not  remain  in  force,  e.g. 

BEETHOVEN:  "Prometheus" 


•". 


T~r~rT 

192.  In  introducing  and  resolving  this  chord,  the  student  is  strongly 
advised  not  to  raise  the  question  of  tonality.  Tonality  can  rarely  be  set- 
tled by  a  single  chord  (much  less  a  chromatically  altered  one)  but  nearly 
always  depends  on  the  context  (p.  154).  In  the  majority  of  cases,  aug- 
mented chords  resolve  to  chords  which  we  recognize  as  either  tonic  or  dominant, 
and  thus  may  be  said  to  be  more  nearly  related  to  some  keys  than  to 
others.  They  are  so  freely  used,  however,  especially  in  modern  music,  that 
it  is  not  always  practicable  to  settle  just  what  is  their  origin.  This  aug- 
mented 6th  chord,  for  instance,  may  be  used  in  all  the  following  keys. 


That  is,  if  the  original  triad  is 


and,  when  it  is  inverted,  the  bass 


is  lowered, 


the  augmented  6th  chord  resulting  would  be  re- 


6  Aug.  6 

lated  to  C  major  or  c  minor.     On  the  other  hand,  if  the  original  triad  were 


HARMONY  185 

which  can  be  found  on  the  fourth  degree  of  /  minor  or  the  sec- 
ond degree  of  Ab  major,  and  the  6th  of  the  inverted  triad  were  raised, 
rarfeg  ^~\  ^ne  augmented  6th  chord  would  be  related  to  /  minor,  (F 

*^       6    Aug.  6 

major)  or  Ab  major. 

193.  We  cite  a  few  examples. 

BEETHOVEN:  2d  Symphony  (Larghetto) 

^   ^ 

&=4=4=      —=**$tt?- 

b 


rr-"i~gT~gf  *  T     —       I  -p»-»-f- — 
ga=g=£SE^^ggEig 


SPOHR:  "Fall  of  Babylon 


MOZAKT:  Symphony  in  G  Minor 
—-          x 


SCHUMANN:  Humoreske,  Op.  30 
fekyr          |      :  ^T-S^1          — C— 

^r-11  b*J          ^fc-        ~^E<' 


T    (•' 


T  *: 


rn  x1-^ 

R^=  ^Ei        ^=^ 


^^ 


--•&!-*-*- 


^r 


194.   These  augmented  6th  chords  are  also  occasionally  used  in  the  2d 
inversion,  generally  as  passing  6-4  chords;  e.g. 


&:fi    Z          — -:— r. 


Observe  the  ftHRincritpd  4th  in  ft1*  ;  thcfiKuririg  for  the?m  nii)tniente<l  chonls  is  0+,  f>+,  4  f. 

4+  5        a 

to   ilisliiiRiiish   them   from    the   inversions  of   triads  and  7th  chords,   in  which    the   01  h  is  nut 
augmented. 


186 


HARMONY 


195.  The  chord  of  the  augmented  6th,  4th,  and  3d. 

A  6-4-3  chord  is  always  the  second  inversion  of  a  dominant  7th  or  of 
some  secondary  7th  chord.  Whenever  the  major  or  minor  6th  of  certain 
6-4-3  chords  is  changed  into  an  augmented  6th  by  the  introduction  of  acci- 
dentals we  have  an  augmented  6-4-3  chord,  e.g. 


Is" 

fV'C 


(M 


(O 


£~ 


{It07  f 
VlVlb 


Aag.  6-4-3 


196.  Observe  that,  however  the  augmented  6-4-3  may  be  formed, 
the  intervals  from  the  bass  are  always  a  major  3d,  an  augmented  4th,  and  an 
augmented  6th;  in  fact  the  true  name  should  be  chord  of  the  augmented  6th,  aug- 
mented 4th,  and  3d. 

Augmented  6-4-3  chords  may  be  erected  on  any  given  tone,  and  as  to 
their  tonality  (from  the  standpoint  of  their  derivation),  they  are  related 
to  the  dominant  7th  chord  in  both  major  and  minor,  or  to  the  secondary 
7th  chords  on  the  2d,  3d,  6th,  and  7th  degrees  in  major,  and  the  2d  in  minor. 
This  is  made  clear  by  examples  (a),  (6)  and  (c)  above.  Like  the  aug- 
mented 6th  chord  they  generally  resolve  either  to  tonic  or  dominant  har- 
mony, although  freer  resolutions  are  by  no  means  uncommon. 


HARMONY 


187 


The  following  example  illustrates  some  of  the  most  frequent  uses  of  this 
chord. 


From  CHADWICK'S  Harmony 
X 


V       i 

^—  -j-  «  •  —  =  === 

a              \                      1 

f.            -C2       .     ..DCS            -ej   ... 

_ffl  J^  
J 

frt- 

4+ 
3 
V'C 


6+ 
4+ 
3 
vu°rC 


197.  The  chromatically  altered  7th  chords  from  which  the  augmented 
6-4-3  chords  are  derived  are  also  found  in  the  fundamental  position,  as 
well  as  in  the  first  and  third  inversions  (i.e.  as  6-5  and  4-2  chords).  These 
positions  are  very  common  in  modern  music  and  their  effect  is  always 
striking.  On  account  of  their  importance,  examples  are  given  of  each. 


QOCNOD:  "  Faust" 


WAONEK:  "  Die  Meistersinger  " 


{  r     •  \\J=>"    \s>- — ^e=f- — H 

:    -    •-•       .    _.       ~ 


In  both  these  examples  we  find  7th  chords  with  a  lowered  5th  in  the  fundamental  posi- 
tion; these  chords,  if  placed  in  the  2d  inversion,  would  result  in  augmented  0-4-3  chords,  e.g. 


In  the  first  measure  of  example  (M  we  also  have  an  aiiKinerited  G— 1-3  chord  on 


188 


HARMONY 


YEBDI:  "Requiem" 


A       Jj-J  4  j 


In  this  last  example  we  find  the  first  inversion  of  a  dominant  7th  chord  with  lowered 
fifth  (p.  173),  e.g. 


In  the  last  chord  of  the  second  measure  is  an  illustration  of  a  very  important  point,  not  only 
in  augmented  chords  but  in  all  chromatic  alterations.  The  chord  is  really  an  augmented  6-4-3, 
and  would  ordinarily  have  been  written; 


in  order,  however,  to  preserve  the  symmetry  of  the  ascending  bass  the  Djj  is  enharmonically 
changed  to  CJ. 

One  more  very  characteristic  example  is  given  of  this  first  inversion. 

CKSAR  FRANCK:  Prelude. 


As  in  the  example  from  Verdi  above,  the  original  chord  is 


-H;   the  5th   is 


lowered  and  the  chord  placed  in  its  first  inversion.  V7 

For  an  illustration  of  the  last  inversion  of  this  chord  we   have  the  following  from  the 
same  Prelude  of  Franck. 

X  X  ^       _ 


HARMONY 


189 


In  the  first  measure  we  see  the  chord    E2zz:Jg=i  B    placed  in  its  third  inversion  (i.e. 

as  a  4-2  chord) ;  in  the  second  measure  the  same  chord  is  used  in  the  more  common  way  as 
a  regular  augmented  6-4-3,  i.e.    ^~~#~ — «•=>     I--*-*?? 


The  following  striking  passage  contains  both  an  augmented  6—4-3  chord,  and  also  the 
first  inversion  of  the  original  7th  chord. 


BRAHMS:  Sonata  In/  minor. 


THE   AUGMENTED   6-5-3    CHORD 

198.  Whenever  the  major  or  minor  6th  in  the  first  inversion  (6-5)  of 
certain  7th  chords  is  changed  by  chromatic  alteration  into  an  augmented 
6th,  we  have  a  chord  of  the  augmented  6th,  5th,  and  3d,  e.g. 


Major  6th. 


Aug.  6th.        Major  Oth.    Aug.  6th.        Minor  6th.     Aug.  Ctli. 


199.  As  to  the  practical  use  of  this  chord,  it  may  be  introduced  in  the 
freest  possible  manner,  provided  the  leading  of  the  voices  l>e  good,  and  it 
is  by  no  means  necessary  that  it  should  be  preceded  by  the  unaltered  6-5 
chord.     Like  the  augmented  6th  chords  just  discussed,  it  has  many  and 
varied  resolutions,  although  some  of  them  are  more  common  than  others 
and  have  more  natural  key  affinities. 

200.  In  regard  to  the  derivation  of  this  chord  (quite  apart  from  its 
entrance  and  progression  in  any  given  context),  the  most  useful  view  is  to 


190 


HARMONY 


consider  that  it  is  the  first  inversion  of  a  diminished  7th  chord  with  a  chro- 
matically lowered  3d.  Many  French  and  German  theorists  treat  all  the 
augmented  chords  as  inverted  forms  of  chromatically  altered  dominant 
harmony.  These  chords  are  often  found  grouped  together  in  passages  like 
the  following: 


i.e.  the  chords  in  (a)  are  derived  from  this  dominant  chord 


and 


those  in  (6)  from  H£§— 


which  is  an  altered  dominant  chord  on  the 


2d  degree  (or  the  dominant  of  the  dominant). 

201.  The  usual  resolutions  of  this  chord  are  analogous  to  those  of  the 
two  other  augmented  chords.  Exceptional  resolutions  will  be  shown  in 
examples. 

(a) 


When  an  augmented  &-5  chord  resolves  directly  to  a  triad  as  at  fa),  the 
consecutive  5ths  so  caused  are  generally  avoided  in  strict  four-part  writing 
for  voices,  although  not  infrequently  found  in  instrumental  music,  e.g. 


PIANO. 


BEETHOVEN:  Sonata  No.  1 
for  violoncello  and  piano 


kf:    fb     £:       f:    f:    fl^ 

-d 7! I        •    I ^^1        »    •     I       »1  •    I »- 

Xufi — i 


CELLO. 


HARMONY 


191 


In  the  following  we  have  two  resolutions  of  this  chord  in  succession; 

SCHUUEKT:  Fantasie,  Op  78 


while  in  the  next  we  are  shown  the  beautiful  effect  producible  by  the  diFerent  chromatic 

•Iterations  of  the  same  tones. 

GOUNOD:  Introduction  to  "Faust" 


|_L_Uas_H_t 

•  =r .  -         rr*=tat=jfcz| 

•r  ,      =»•  r  r  »  y 


r 

In  this  augmented  6th  chord  the  student  must  constantly  be  on  the  watch  for  changes 
in  notation,  as  when  the  chord  resolves  to  a  major  6-4  chord  the  perfect  5th  is  almost  always 
written  as  a  doubly  augmented  4th,  e.g. 

X 


I 


6 
4 

i.e.  DJ  is  written  instead  of  EJ?  in  order  to  preserve  the  symmetry  of  the  ascending  soprano. 

The  following  passage  is  a  beautiful  example  of  this  doubly  augmented  4th;  the  resolu- 
tion also  is  somewhat  unusual  —  to  the  first  inversion  of  the  submediant  triad. 

SCHUMANN:  Novcllette,  Op.  21,  No.  7 
I 


202.    From  the  outset  the  student  must  recognize  the  fact  that  any 
augmented  fr-5  chord  is  in  sound  identical  with  a  dominant  7th  chord;  e.g.  if 

(a)_ 

this  chord   F^  &<^      ^  be  played  by  itself  we  cannot  tell  whether  an  aug- 

C  VI? !><9?  — — ^ 

(/<)  _ 
mented  chord  is  meant  or  a  dominant  7th   [/£   nf*      ^   (,,  94)      Great  use 

t  V2      a^ J 

is  made  of  this  enharmonic  relationship  in  modulating  between  remote  keys 


192 


HARMONY 


(c/.  Chapter  XLV),  for  obviously  chord  (a)  can  be  approached  from  several 
of  the  sharp  keys,  e.g.  G  and  D,  and  with  the  implied  enharmonic  change 
(6),  can  be  directed  toward  Ai?,  Db,  /,  etc.  The  student  should  look  up  for 
himself  examples  of  this  modulation  in  standard  compositions. 

203.  Like  the  two  preceding  chords,  the  augmented  6-5  chord  is  very  common  in  the 
fundamental  position  (i.e.  as  a  7th  chord  with  a  diminished  3d)  and  also  in  the  two  other  in- 
versions (4-3  and  2).  Examples  are  cited  of  each. 

WAGXEB:  Prelude  to  "Lohengrin" 
X 


x^f  y 


In  this  passage  we  find  a  chromatically  altered  7th  chord  used  in  the  fundamental  posi- 


tion. 


This  chord  placed  in  the  first  inversion  would  give  a  regular  augmented  6-5,  e.g. 


The  introductory  chords  of  Schubert's  wonderfully  dramatic  song  "Am  Meer"  furnish 
,  striking  example  of  this  chord  in  the  second  inversion. 

X  ^ 

i 


Here  we  see  another  case  of  the  enharmonic  notation  spoken  of  above,  for  DJ  is  written 
instead  of  Et?  on  account  of  the  upward  resolution.     The  7th  chord  in  its  original  position  is 

p2C — -S^^-tS  — -I    and  with  the  original  5th  in  the  bass  is  obviously  used  as  a  4-3  chord. 

try — g^ — frg — j 

The  passage  might  also   be  explained  as  a   normal   augmented  6-5  chord 
on  a  tonic  pedal-point. 

The  following  passage  gives  us  both  the  third  inversion  (chord  of  the  2d) 
and  another  second  inversion,  the  original  chord  being 


HARMONY 


193 


CHOPIN:  Nocturne,  Op.  15, No.  3 

J          I  I 


204.  Now  that  the  fundamental  facts  in  regard  to  this  chord  have  been 
presented,  its  use  will  best  be  learned  by  a  careful  analysis  of  examples 
from  musical  literature.  A  few  are  cited  and  others  should  be  sought 
for.  A  thorough  knowledge  of  all  the  augmented  chords  is  indispensable 
for  an  insight  into  the  subtle  harmonies  of  modern  music. 

SCHCBEKT:  Impromptu,  Op.  142,  No.  2 


c 

SCHUMANN:  "  Bunte  Blatter,"  Op.  99,  No.  H 


The  above  passage  is  unique  in  its  abundance  of  augmented  harmonies,  both  in  funda 
mental  position  and  in  inversions.    Observe  that  the  first  two  measures  are  on  a  double  |>e  bl. 


GOUNOD  :  "  Faust,"  Act  I 

( 


"  Faust,"  A.-t  III 


These  la.st  examples  are  interpstiriK,  the  formpr  on  account  of  the  downward  repclution 
of  the  auKmenled  interval,  the  latter  for  the  combination  of  a  suspended  tone  with  the  third 


inversion  of  an  altered   7th  chord,  e.g. 
lilt  ion. 


Ol>!»ervc  the  subtle  chromatic  reso- 


194 


HARMONY 

TSCUAIKOWSKI:  6th  Symphony  (1st  Movement) 


tf^ifl 

_..,. 

—  1  —  '  •  j   j  fj    ,r^^«2 

H 

; 

P 

-i^P^:     =f=^=^= 

*~    n 

J 

I      I  '    1       . 

etc. 

£C. 

&3=£       I 

HTT        F-      _ 

=fc     rf    |^    -^    -L-J-TSU 

"•  '"    '  ~z    r   j  —  ""  —  -  ^?" 

< 

M 

In  the  passage  from  Tschaikowski  observe  the  bold  downward  leap  of  the  lib. 
DVOBAK:  "New  World"  Symphony  ( 2d  Movement) 


In  analyzing  this  beautiful  phrase  of  Dvorak,  let  the  student  ask  himself  what  is  the 
position  of  the  chord  and  also  explain  the  notation. 

205.  In  harmonizing  melodies  (Chapter  XL,  Kx.  7-24)  It  Is  helpful  to  know  that  the 
augmented  6,  augmented  6-4-3  and  augmented  6-6  chords  are  frequently  to  be  derived  from 
inversions  of  the  fourth  triad,  second  chord  of  the  7th  and  fourth  chord  of  the  7th,  respec- 
tively, of  the  minor  scale,  their  ordinary  resolutions  being  the  following  (but  cf.  §§  192, 196, 
198,201). 


The  student  is  reminded,  however,  that  these  chords  are  derivable  in 
various  ways  (§§  192,  196,  198);  THEY  ARE   THEREFORE  VERY  USEFUL  IN 

MODULATION. 


CHAPTER  XL 


EXERCISES  WITH   AUGMENTED   CHORDS   AND   THEIR   INVERSIONS 


6+ 

' 


206.  AUGMENTED  triads  being  marked  by  a  X,  the  same  method  is  pursued  with  the  aug- 
mented chords.     A  distinction  is  thus  made  in  figured  basses  between  these  chords  and  such  as 
are  indicated  by  f ,  4,  f  (§  194).     In  the  soprano  melodies  some,  not  all,  of  the  augmented  chords 
6  4 
3 

are  marked  by  a  X ;  in  a  few  of  the  bass  melodies  they  are  also  indicated  in  the  same  way, 
figures  not  being  given  in  Ex.  7-10-    Augmented  skips  are  permitted  in  any  voice. 


HARMONY 


195 


^--     rg- 


7       6          6+       tJ  £  6 

2 


6          6+6—        q 
454  — 


2. 


0 


4     — 

3     — 


26$  6      4     $     £     6    6B  6 

24  42  4 

3  3 


:f*-rfr 


-6M- 


3       4     6+   6fl 

4      5fe    4 


6+       f      6        6        2 

4+  5JJ      4 

3 


4,  6+    6     7  — 

39  54:,? 


4. 


-*^— ^ 

6      |  6      5fl 
5  4 


F 


^  * 


6+676        Jf*66b     6-4 
54  4  2  4— 


5. 


6 

4+ 
3 


6+6 
64 


8        III+       6+       6 

5         9 


6 


3  76*6    6b65tJ  6      6+ 

4      2  48  & 

7.    (Hymn  tune) 


$6         66$ 
5     4 


EiMfl 


S: 


196 


HARMONY 


9. 


10. 


^3±r« 

.  ...  _   .. 

--  ^r-  u  ; 

1 

1 

,    r     .  r  .    . 

X  X 


11.     (Hymn  txine) 


In 


-(4  voices  unison) —  — (In  parts) 


12.     (Hymn  tune) 
x 


InC. 


In  a. 


13.     (Chant) 


HARMONY 


197 


14.     (Hymn  tune) 


In/- 


In  Ah. 


2EE 


15. 


In/- 

x 


-In  Ab. 


=tzn 

^ 


16. 

fe 


.'Ill     IT 

d     ^      sJ— ' 


-(2 (SL 


17. 


•2- 

f-H-:,,: 


In  d  —    —  In  a. 


18. 


- 


In  F- 


198 


HARMONY 


19.  Open- 

Allegro. 


-Open— 


=*rnr  HY~  ru  M-*=& 


-Close  Open- 


20. 


InF- 


In  a- 


Ind. 


EXERCISES  FOR  THREE  VOICES.     The  4+  chord  can  be  used  by  having  a  voice  sing  as 
follows  (§200): 


4f  3  34+ 


Augmented  chords  are  marked  by  a  X). 
21. 


22. 


P 


In  e 


In  C 


23. 


In/ 


XXX 


1 


HARMONY 


199 


MEE^=J4f=f=-T=f^— >«M^=  3 


CHAPTER  XLI 

SUSPENSIONS 

207.  HERETOFORE  in  our  work  all  the  voices  have  progressed  simul- 
taneously from  one  chord  to  the  next,  although  one  or  more  of  the  tones 
were  often  harmonic  factors  common  to  each  chord  and  sometimes  held 
over  into  the  second  chord  from  the  first  one.  We  must  now  become  fa- 
miliar with  a  rhythmic  device,  by  which  the  prolongation  of  tones  into  a  chord 
to  which  they  do  not  belong  delays  the  entrance  of  one  or  more  of  the  logical 
factors  in  that  chord;  in  other  words,  parts  of  two  different  chords  are  momen- 
tarily heard  together,  and  the  dissonance  and  rhythmic  disturbance  caused 
by  this  harmonic  dislocation  are  felt  to  be  logical,  when  the  delayed  voices 
move  on  to  the  tones  which  would  otherwise  have  originally  been  sounded. 

If,  e.g.  instead  of  having  the  voices  move  as  follows, 


1  »  A 

we  delay  the  entrance  of  the  3d  in  the  second  chord  by  holding  over  the  F, 

(a)          (ft)        (c) 


IV  I 

while  the  other  voices  proceed  to  their  positions  in  the  next  chord,  a  gen- 
uine suspension  is  formed,  in  which  the  dissonant  anil  rhythmic  elements  are 


200  HARMONY 

plainly  felt.1  Thus,  in  the  preceding,  the  tone  F  is  delayed  in  its  progression 
to  E  by  being  smjicnded,  while  the  rest  of  the  harmony  changes.  The 
entrance  of  such  a  tone  as  part  of  the  first  chord  is  called  the  preparation 
(a);  the  holding  it  over  into  the  following  chord  to  which  it  does  not  be- 
long is  the  suspension  itself  (b);  and  the  ultimate  progression  of  the  sus- 
pended tone  to  its  proper  place  in  the  chord  is  the  resolution  (c). 

208.  Suspension,   like   chromatic   alteration,    is   a   principle   of   very 
broad  application,  and  our  best  approach  to  the  subject  is  the  general 
statement  that  a  suspension  may  be  formed  by  delaying  the  downward  or 
upward  progression  of   any  factor  of  a  triad,  or  seventh,  or  ninth  chord; 
this  effect  may  take  place  in  any  voice  and  in  any  position  of  the  chord, 
fundamental  or  inverted.     When  the  examples  are  studied  it  will  be  seen, 
however,  that  some  of  these  suspensions  are  much  better,  and  hence  more 
common,  than  others. 

209.  The  laws  governing  the  use  of  suspensions  are  few,  and  extremely 
logical  and  simple;    but  a  thoroughly  artistic   handling  of  them  is  ac- 
quired  only  by  considerable  practice.     It  is  obvious  that    the  suspended 
tone  must  invariably  be  prepared  in  the  same  voice  in  which  it  is  to  be 
sounded  as  the  dissonance;  e.g.  if  we  write  (a)  instead  of  (6),  we  have  no 
suspension  at  all,  but  an  appoggiatura  (Chapter  XLIII). 


(a) 

*ffi£      SP 

X                           ("  ) 

|J     J    nJ= 

g!     J    II 

EBEjl  — 

A 

fi££t= 

-a,  ||-»  — 

•Si                    J 

pi   r 

L_  ^  a 

This  effect  is  sometimes  called  an  unprepared  suspension,  although  such  a  paradoxical 
term  is  questionable. 

210.  There  is  an  old  rule  which,  in  one  form  and  another,  still  ap- 
pears in  books  upon  harmony.  As  given  in  a  recent  treatise  it  is  as  follows: 
"If  the  suspension  be  tied  to  its  preparation,  the  latter  should  be  of  at 
least  equal  length  with  the  suspension;  it  may  be  longer,  but  must  not  be 
shorter.  When  the  suspended  note  is  sounded  again,  this  rule  is  not  so 
strictly  observed." 

This  academic  rule  is  too  sweeping,  and  is  not  justified  by  the  practice 
of  composers;  it  should  therefore  be  abandoned.  The  strongest  statement 
that  can  rightly  be  made  is  that  in  a  large  majority  of  cases  the  tone  of 
preparation  is  at  least  as  long  as  that  of  suspension,  and  that  the  rhythmic 
effect  attained  in  that  way  is  usually  better.  In  the  following,  the  tone 
of  preparation  in  (a)  and  (6)  is  shorter  than  that  of  suspension,  while  in 
(c)  it  is  of  the  same  length. 

1  By  some  theorists  those  suspensions  which  resolve  upwards  are  called  Retardations; 
but  this  term  is  an  unnecessary  fineness  in  classification. 


HARMONY 


201 


BEETHOVEN:  Sonata,  Op.  2,  No.  1 


BRAHMS:  Variations 
on  a  theme  of  SCHUMANN'S,  Op.  9 


SCHUMANN  :  Romanze,  Op.  28,  No.  2 


211.   Suspensions  generally  occur  on  an  accented  beat,  or  on  the  ac- 
cented portion  of  a  beat,  the  resolution  being  unaccented; 

x          x 


but  it  is  not  necessary  that  such  should  be  the  case,  for  the  following  are 
true  suspensions,  though  unaccented: 


212.  As  a  suspended  tone  is  merely  a  temporary  substitute  for  the 
harmonic  tone  that  follows  it,  no  progression  which  would  be  incorrect 
without  a  suspension  is  justified  by  its  presence.  Care  should  therefore  he 
used  in  leading  another  voice  in  similar  motion  to  the  tone  of  resolution.  The 
8ves  and  5ths  in  (a)  and  (6)  are  quite  as  bad  as  they  would  be  in  (r) 
and  (</). 


' 


'  _J 


-/S~  J=l- 


1-      ri 

__t . — u — ; 


202 


HARMONY 

(rf)  (e) 


good 


In  regard  to  consecutive  5ths,  however,  some  theorists  allow  considerable  latitude  when 
the  suspension  is  in  an  inner  voice. 

HAYDN:  "Creation" 


It  is  seen  that  the  effect  in  the  extract  from  Haydn  is  softened  by  the  predominance  of 
the  7ths;  the  first  example  is  not  recommended. 

213.  As  the  dissonant  element  is  of  prime  importance,  a  really  good 
suspension  should  form  a  dissonance  of  a  7th,  a  2d,  or  a  9th  (the  same  as 
a  2d  in  the  octave  above)  with  some  one  of  the  integral  tones  of  the  chord; 
e.g.: 


7th. 


9th. 


Suspensions  without  this  element  are  generally  weak  and  without  charac- 
ter, although  good  where  they  occur  interspersed  with  other  stronger  ones 
(§  224),  e.g.: 

Much  stronger. 


The  leading  of  the  voices  may  result  in  a  suspension   to  the  3d  without  the  presence 
of  one  of  the  dissonances1  mentioned  above;  this  is  good,  even  if  not  so  strong  as  it  might  be; 

X 


1  Some  theorists  have  maintained  that  what  we  call  the  perfect  4th,  while  not  a  disso- 
nance, is  still  not  a  perfect  consonance,  as  it  does  not  give  a  feeling  of  finality.  F6tis  goes  so 
far  as  to  make  yet  another  subdivision  for  it  in  classification,  under  the  name  of  "  mixed  conso- 
nance." This  question  is  worth  looking  up  by  the  student.  One  thing  is  clear,  that  the  4th 
in  the  example  given  does  demand  a  resolution  downward  quite  as  decidedly  as  would  a  7th. 


HARMONY 


203 


it  may  be  changed  thus,  if  preferred. 


In  this  connection  the  difference  should  be  clearly  understood  between 
a  note  held  over  as  the  preparation  of  a  secondary  7th  chord,  and  a  real 
suspension.  In  the  former  case  we  can  always  classify  the  factors  as  1, 
3,  5,  7,  and  the  resolution  is  to  a  new  chord  (§  219)  ;  in  the  latter  the  sus- 
pension forms  no  part  of  the  chord  and  is  resolved  while  the  rest  of  the  chord 
remains  (but  cf  §  216),  e.g.: 


Not  a  real  suspension. 


Suspension  to  3d. 
X 


NOTE.  —  It  is  questionable  whether  the  so  called  suspensions  of  the  chord  of  the  9th 
(§  §  157-161,  Ex.  2,  3,  6,  8b,  and  §  165,  Ex.  a)  should  be  regarded  as  genuine  ones  ;  for  it  can  be 
reasonably  argued  that  the  9th  does  form  an  integral  part  of  the  suspended  chord,  and  that 
the  definition  and  idea  of  suspension  are  not  strictly  carried  out.  The  chord  of  the  9th  may  ih 
such  cases  be  perhaps  more  properly  said  to  be  prepared,  as  chords  of  the  7th  are  prepared. 

214.  Practically  the  only  subtle  point  in  the  treatment  of  suspensions 
is  to  know  just  when  the  tone  of  resolution  may  be  anticipated  in  some 
other  voice.  For  the  student  it  is  safe  to  say  that  such  anticipation  should 
generally  be  avoided;  although  here,  as  in  other  matters,  there  is  a  great 
difference  between  strict  four-part  writing  for  voices  and  free  instrumental 
music.  There  is,  however,  a  great  difference  of  treatment  between  sus- 
pensions before  the  third  and  those  before  the  root.  The  rule  as  to  non- 
anticipation  of  the  tone  of  resolution  is  also  much  stricter  when  the 
suspension  (especially  of  the  third)  is  in  the  bass,  than  when  in  the  other 
voices;  e.g.  the  following  should  never  be  written, 


is  good. 


With  the  suspension  to  the  root  in  the  bass  we  sometimes  find  passages 
like  the  following: 


204 


HARMONY 


although  the  effect  is  somewhat  harsh. 

An  analogous  passage  is  cited  from  Beethoven,  in  which  a  tone 
lution  in  an  inner  voice  is  anticipated  in  the  soprano,  e.g.: 


reso- 


215.    The  resolution  to  the  root  in  the  soprano  is  of*  m  anticipated 
in  any  one  of  the  other  voices,  even  in  an  inner  one,  e.g. : 

Good.  Good.  Good. 


Care  should  be  taken  to  have  this  anticipation  at  least  nine  degrees 
distant  from  the  tone  of  suspension;  the  two  tones  should  never  appear  simul- 
taneously within  the  same  octave,  e.g.: 

Bad.  ,    Bad. 


J.      £= 


With  a  suspension  before  a  3d,  the  3d  may  often  be  anticipated  in 
a  lower  voice,  provided  that  the  anticipation  l>e  nine  degrees  distant 
from  the  suspension. 


HARMONY 


205 


the  following  quotation  is  a  case  in  point. 

BEETHOVEN  :  Sonata,  Op.  14,  No.  1 


EpT—^^S    3 
ffM_^      '^3=  3 


Such  combinations  as  these,  however,  would  be  entirely  erroneous: 

Bad.  Very bad- 


When  a  suspension  takes  place  before  the  leading  tone,  the  latter,  for  an 
obvious  reason  should  never  be  anticipated. 

Always  bad. 


216.  At  the  same  time  that  the  suspension  resolves,  the  rest  of  the 
harmony  may  be  changed  by  chromatic  alteration,  or  by  various  moans 
which  do  not  interfere  with  the  suspension  itself,  e.g.: 


_ 
•    ^  II    *^*~l 

=Erfe*:_*--l 


on  this  point  a  study  of  the  overture  to  "Die  Meixtcrxinycr"  will  be  profit- 
able. 

217.  The  suspended  tone  may  even  abandon  its  resolution  altogether, 
and  be  merged  in  the  following  harmony;  it  also  is  occasionally  resolved 
chromatically,  e.g.: 


206 


HARMONY 


J.  A    ~ 


218.  The  resolution  of  a.  suspension  is  often  delayed  by  the  interpola- 
tion either  of  other  tones  belonging  to  the  chord,  or  of  passing  or  auxiliary 
tones  which  form  an  embellishment  to  the  tone  of  resolution,  e.g.: 


-t^- 


-i I- 


f 

the  following  examples  illustrate  this  free  resolution. 

HAXDEL:  Suite  No.  3  (in  D  minor) 


^ 


etc. 


HARMONY  207 

BEETHOVEN:  Sonata,  Op.  10,  No.  1 


219.  Suspensions  are  often  used  in  more  than  one  voice  at  a  time; 
m  fact  all  the  parts  but  one  may  be  held  over.  Triple  suspensions  are 
frequent  in  the  authentic  cadence,  both  in  introducing  the  6-4  chord  and 
before  the  final  tonic  chord,  e.g.: 


f5 


..I: 

-'•j  ~- — i      i  ^    -«•- 
•MI 


-f—<s>— — n~*        i-15*- 


-»-4 — • *-f 

=^=P 

On  looking  back,  the  analogy  will  be  seen  between  the  following  sus- 
pensions and  chords  of  the  9th,  llth,  and  13th. 


Quadruple  Suspension.    Quintuple  Suspension. 

U — ..  I          I 

^=:§^r^— g     ft 

— ft '<a-^.cs^--Z.- 

T 


iSC>-f- 

i  ^-^i        i 


^d^i  J 

i  ^" — _,  L~ 

£=£: 


NOTE.  —  A  succession  of  inversions  of  chords  of  the  7th  may  occur,  in  which  at  first  sight 
we  seem  to  have  a  series  of  suspensions; 


=rr  —     -i_ -fj-zr^rT:,-. 

si  \* 
j  j.  j  j  j  j  : 

~ 


these,  however  are  not  (tenuine  suspensions  (§  213). 

220.   The  student  will  acquire  indispensable  practice  by  making  out 
for  himself  a  table  of  all  possible  .suspensions  before  the  factors  of  triads, 


208 


HARMONY* 


and  of  seventh  and  ninth  chords,  in  different  positions  and  in  various  voices. 
A  few  of  the  most  frequent  suspensions  are  herewith  given  and  also  some 
of  the  less  usual  combinations. 

221.    Suspensions  before  the  root  of  a  triad  from  above  and  below. 


2_™       ^ K-   

>2-«  - 


etc.,  good  in 
all  voice*. 


In  a  chord  of  the  6th. 

lg"^~^ 
/_  ^i 


9  8 


good  in  all 
voices. 


9         8 
In  a  6-4  chord. 


etc.,  in  all 
voices. 


7          6 


Seldom  used. 


5          4 


etc.,  in  all 
voices. 


a.          (=*- 


1         8 


In  a  chord  of  the  6th. 


s-^ 


etc. 


5  6 

In  a  6-4  chord. 


5  6 


etc. 


3        4-43 

S22.   Suspensions  before  the  third  of  a  triad  from  above. 

In  a  chord  of  the  6th.  In  a  6-4  chord. 


etc.,  in  different 
voices. 


4      3 


etc. 


5       — 

2       — 


9      8 
6     — 


7      6 
4     — 


HARMONY 


209 


223.    Suspensions  before  the  third  of  a  triad  from  below  are  rather  rare;  nevertheless 
they  are  perfectly  possible  and  sometimes  of  striking  effect,  e.g. 


Seldom  used. 


224.    Suspensions  to  the  5th  of  a  triad  from  above  are  weak  and  seldom  used  except  in 
connection  with  other  genuinely  dissonant  suspensions  (§  213). 


x    Good. 


^nSE±5 


* 


6        5 


E^EE  =sp=r-r. 

^zzz- L_^_-  i^EE 


9865 
4         3 


~T      7 
4 


Suspensions  to  the  5th  from  below  are  often  of  great  value,  especially  in  the  case  of 
7th  chords;  in  (a)  and  (6)  the  G  is  a  5th  (or,  inverted,  a  4th  below)  from  C,  the  root. 


>••  ••>  r—^ — 


225.  Before  the  intervals  of  a  dominant  7th  chord,  suspensions  l«>th  from  above,  and 
in  a  somewhat  les.s  decree  from  below,  are  very  effect ive  and  niurli  use<l.  A  table  is  easily 
made  out.  A  few  model*  are  given. 


Before  tli«  root. 


-210 


HARMONY 


For  suspensions  before  the  third  of  a  dominant  7th  chord,  cf.  the  preceding  table  of 
triads  (§§  232-223). 

Before  3d  from  below. 

I L 


226.   Suspensions  before  the  5th  of  a  dominant  7th  are  much  stronger  than  in  the  case 
of  a  plain  triad,  and  are  very  frequent. 

Chromatic  resolution. 
X 


227.  Suspensions  before  the  7th  itself  have  to  be  handled  with  considerable  skill  in  order 
that  a  genuine  dissonant  effect  may  be  produced.  At  best,  suspensions  before  the  interval 
of  a  7th  are  stronger  in  connection  with  a  diminished  7th  chord  than  with  a  dominant  7th. 


H  -    - 

g  II  ~— Hr=»—  =4=^=^ 


VII07 


228.  Suspensions  before  the  different  factors  of  diminished  7th  chords,  of  chromatically 
altered  chords,  and  of  all  the  augmented  chords,  are  good  and  of  frequent  occurrence.  The 
following  quotation  will  illustrate  these  and  other  effects. 


WAGNER:  "Tannhauser" 


From  the  same 


HARMONY 

Cf  SAB  FRAVCK 


211 


*& 


--c  -i 


col  Sva, 
In  these  passages  we  see  suspensions  before  diminished  7th  chords;  in  (6)  the  bass  is  a  tonic 

pedal. 

WAGXEB  :  "  Die  Walkure,"  Act  2,  Scene  4 
X  X  s* 

^^T^Y*  rf*  "*^ 


=^gl=i 

a  _J 1 :    I E 


r 

VERDI  :  "  Aida,"  ( Finale  of  Act  2) 


<b»iq  *-M»wf  r  r^r 

ssp±         LJ  -LB^E 


fefr-4  -|: 

— •*»  l?4    i  _ 


_| tf-  f_      _tj- 

EirE:  =*=     3RE1 


<5 


£   fe    g    g  «g    £ 

^5 ^r — b»r *- *- fifc. 

•b"L        j-          l  I    '*-'' '.  . — 


I 


In  the  above  interesting  passages  we  find  augmented  harmonies  qualified  by  suspen- 
ions.     The  following  quotations  sh:)W  a  bold  use  of  suspensions. 

TsniAiKowsKi  :  Cth  Symphony,  last  movement 
X 


X  __± — -3  X  l          XJ _  N i 

^  ^^|ps=::-S^pi^5?;^:::i.  ;^-: 


etc. 


\_    _£__ 


212 


HARMONY 


STRAUSS:  "Todund  Verklarung' 
j^       8va- 


CHAPTER  XLII. 

M9.  (In  6-10  the  X  indicates  where  &  suspension  is  intended;  the  same  sign  is  employed 
in  a.  few  instances  with  the  soprano  melodies,  but  suspensions  are  to  be  used  in  these  in  many 
cases  where  there  is  no  X.  Do  not  confuse  true  suspensions  with  prepared  chords  of  the  7th.) 

1. 


5  —  98  6—  98          5 6 

43  43  4—    3 


4    3 


2.    Espressico.  Open — • Close- 


-Open 


65—  2766  98975—  66— 

43  6-7  43  546 

4—3  2    — 


-Close. 


Open. 


11  f    f      6  6    J      7$3      2       76-^f     6       5    —      6     7    76     7  — 

9  2  5  5  4+5fl43  4—65 

5  43  3  — 


3. 


^ 


±±^±^=J=^F. 


3        e  7 11  5 

5 9  4—3 

4—  3 


7b         5-- 
5.          4—  3 


m 


HARMONY 


213 


4.        Close. 


=*= 


glllllp: 


7          9— 32       6      6  5— 

7 5  43 

4  —  3 


7  9898 
6—7  — 
4—  3  — 


5.  Open.  Close- 


i    J'  W     A    i 

—  , 

| 

£3 

1                     [ 

\_s    l|/    & 

-J-*- 

jg 

1  

-|  _J— 

36  76  76  98  11         36665          67          5  — 

4—6  9  54  43 

3—  5 

6.     Open.     Close, 
x 


7. 


X 


&±??=Z2: 


F 


X 
+^+ 


f^ 


Vh. 


8. 


II 


9.  Open. 

m    J* 

x 

x 

X 

1       1 

X 

C\*  i\      f    fl> 

1 

1 

i    II 

J*  '» 

^>    * 

* 

-1*     & 

Z    Lf 

31 

J     1      1 

m 

^r  IJ 

10.  Open.     Close. 


x . x_          OpenJ 

pfe^:  ^t=3^J=  ^M^Ej^=         =*-£ 

I "ff~        z~^~  ~^*~  — y~~        — » 


-lu  D. 


11. 


II 


12.  Allegro. 
( )pen- 


t_>  • 


214 


Close- 


HARMONY 

Open 


-Close- 


S 


, 


In  e. 
— Open- 


Iu&. 


In  D. 


-Close 


' 


InG. 

— Open- 


In  C. 


In  a. 


InG. 


3  . 


-C  1  ose Open . 

x 


13.     (Chant)  Close- 

fc 


In  c. 


-  y  ,  v  b 

r 

'O'                            ^^ 

>r  b  h17      c/ 

1 

^           (3 

f 

1*2 

Iii  Ab. 
14.     Allegretto 


Ef^g^rj^j^ 


In6>- 


-luDb. 


15.     (Hymn-tune) 


g|^^J-.l4f=F=^I^E^E^p1 


p^F^r^r^^1^^ 


InBb. 


In  y. 


HARMONY 


215 


16.     (Chant) 
x 


In  D.  In  G. 


17.     (Hymn  tune) 


^=Z=l=i 


=F3=t=5= 


3t=3t 


^^    :  I 

— & & — 


InE. 


II 


In  A. 


18 


i 

--  U 


-L 


Open- 


-Close- 


19. 


Allegretto.       x 


^Illlllil^Slllfll^t 


20. 


Jl 


21.     Allfyrctto. 

"~" 


• 


rp 


: 


In  F- 


216 


HARMONY 


Ill 


' 

r-Ff 


Ind- 


-Iii  Kb. 
x 


In  li  . 


3: 


II 


111  C. 


L> 


23. 

u    Allegretto. 


J    ' 


m 


24. 


Expressive.*  x 


In  e. 


x       x 


/-\U  N <^^SA  |  |  |  ^0f 


In  D.  In  6. 

EXERCISES    FOR    THREE     VOICES 


25. 

H>-8 


HARMONY 


217 


m 


P— p=^ 


•"**  •  ttJ  ~*~ 

1        ^^      I     i — i 


InC. 


*—*—+ 


£=J= 


CHAPTER  XLIII 
ORNAMENTAL  TONES 

PASSING-TONES:    AUXILIARY    TONES:    CHANGING  TONES:    APPOGGIATURAS: 
ANTICIPATION:  MELODIC  FIGURATION. 

230.  THE  PASSING-TONE  has  been  defined  (§§  103,  147).  It  may  be 
diatonic  (a),  or  chromatic  (b)  (c),  accented  (r),  or  unaccented  (a)  (/)) ;  the 
two  tones  between  which  it  occurs  may  belong  to  the  same  or  to  different 
chords. 

00 

(«)   x  ( i>)  x  x          — 


r  *?  ^ 
j  -J   j 

:.T  J     J^  \S       '    \\'l   (-    * 

r 


-  ^  :^iL^' 

r      ',  j 

J     J  ^ 

i^~  || 


The  interval  to  be  filled  out  melodically  may  rccjiiire  more  than  one 
passing-tone  ((f)  (e);  these  tones  may  also  occur  in  two  or  three  voices  sim- 
ultaneously (r) 


218 


HARMONY 


By  some  theorists,  the  passing-tones  in  (e)  would  be  considered  as  forming  passing  chordi; 
this,  however,  is  purely  a  question  of  definition.  The  same  is  true  when  auxiliary  tones  or 
appoggiaturas  occur  in  several  voices  (§§  232,  234,  238). 

231.  In  §  103,  it  is  said  that  no  consecutive  8ves  or  Sthsmay  be  allowed  to  result  from 
passing-tones.  It  should,  however,  be  pointed  out  that  such  5ths  do  sometimes  occur  in  the 
music  of  great  composers:  e.g. 

MENDELSSOHN  :  Chorale  in  "  St.  Paul " 


Such  cases  are  to  be  regarded  as  exceptions.  When  these  5ths  are  accidentally  made,  it  is 
possible  and  better  to  change  the  passage,  even  though  the  error  be  a  purely  technical  one; 
e.g.  (a)  changed  as  in  (6). 


(a) 


232.  THE  AUXILIARY  TONE  (§  104)  is  unaccented,  and  proceeds  up- 
ward or  downward  from  its  principal  tone  by  a  major  or  minor  second  (a), 
returning  to  that  tone;  it  may  also  occur  in  two  or  three  voices  simulta- 
neously (6)  (§  230). 


When  it  is  below  the  harmonic  tone,  it  may  be  chromatically  altered  with- 
out affecting  the  harmonic  progression  (c) ;  not  so  if  it  be  above  the  har- 
monic tone  (rf).  At  (e)  we  have  what  looks  like  an  exception,  but  G  is 
really  not  an  altered  tone,  as  we  here  are  using  the  form  of  the  minor  scale 
without  leading-tone  (§§  22,  64). 


HARMONY 


219 


The  following  is  not  an  auxiliary  tone,  but  an  appoggiatura,  being  accented. 

X 


233.  THE  CHANGING  TONE  is  an  unaccented  tone  foreign  to  the  chord 
with  which  it  appears,  and  not  necessarily  a  part  of  the  following  chord  (a) ; 
it  usually  moves  over  a  skip  of  a  3d  (b). 


234.  THE  APPOGGIATURA  is  denned  in  §  166;  it  is  a  tone  foreign  to 
the  chord  with  which  it  occurs,  and  enters  by  step  or  by  skip.  It  may 
enter  from  above  or  below,  and  moves  a  2d  up  or  down,  diatonieally  or 
chromatically,  being  either  accented  or  (occasionally)  unaccented;  it  is  most 
often  of  the  same  length  as  the  tone  which  it  precedes,  but  may  also  !><> 
either  shorter  or  longer  than  the  latter;  it  may  appear  in  any  voice,  and 
indeed,  in  two  or  three  voices  at  the  same  time  (§  230).  IT  PIFFKHS  FHOM 

THK    SUSPENSION    IN    NOT    BEING     IMIOI.ONGKI)    FROM    THE    PHECKDINC,    CHOltl>. 


220  HARMONY 

It  may  appear  as  an  altered  tone  in  one  voice  against  the  same  tone  unaltered  in  another 


|£J— . (-— 


Consecutive  5ths  like  the  following,  produced  by  appoggiaturas,  are  found  in  the  works 
of  the  great  composers,  and  are  unobjectionable  in  their  effect. 


In  the  next  illustration  we  have  what  may  be  properly  termed  a  double  appoggiatura. 
X    X  XX 


In  the  familiar  Rondo  of  Weber's  Sonata,  Op.  24,  there  are  many  passing-tones  and 
appoggiaturas. 

235.  In  the  following  examples  of  appoggiaturas  (x)  in  an  inner  voice  we  see  how  freely 
they  may  enter;  the  resulting  harshness  is  atoned  for  by  our  satisfaction  in  their  resolution. 


(Suspension) 


(Suspension) 


uBff^ueiuuj  ji  i  i 

L-    o-L 


s 


Passages  like  the  following  are  easily  explained  as  containing  appoggiaturas  in  more 
than  one  voice  (or  appoggiatura  chords,  if  that  name  be  preferred.) 

CHOPIN:  Nocturne,  Op.  15,  No.  1 
X 


HARMONY 


221 


The  ornaments  so  common  in  pianoforte  music  of  the  time  of  Bach  (cf.  his  Suites  and 
Partitas)  can  generally  be  explained  as  derived  from  the  above  ornamental  tones.  The  trill, 
e.g.  is  nothing  but  the  repetition  of  a  group  with  an  auxiliary  tone. 

236.  THE  ANTICIPATION  (the  opposite  of  suspension)  is  made  by  an 
unaccented  tone,  usually  shorter  in  value  than  the  following  one,  which 
moves  to  its  appropriate  tone  in  the  next  chord  in  advance  of  the  other 
voices.  It  may  also  occur  in  two  or  three  voices  at  the  same  time;  but 
when  all  four  voices  move  to  the  next  chord  in  this  manner,  the  effect  is 
rhythmic  and  not  harmonic,  and  we  do  not  have  a  real  anticipation. 

Kot  a  true 

X  anticipation 

[__>  J  x 

-  *  •       +—<*>— n :— n 


A  voice  may  anticipate  by  first  moving  to  a  tone  of  the  new  chord  different 
from  the  one  to  which  it  finally  goes  (see  the  example  from  Grieg.) 


237.  MELODIC  FIGURATION:  by  this  term  is  understood  the  embel- 
lishment of  a  melody  in  any  voice  by  the  employment  of  the  various  non- 
harmonic  tones  with  which  we  have  been  dealing,  as  well  as  of  harmonic 
tones   (e.g.  the  arpeggio).     Scale  passages,  being  extensions  of  groups  of 
passing-tones,  are  much   used.     Excellent  examples  will  be  found  in  till- 
slow  movements  of  Beethoven's  5th  and  9th  symphonies,  in  the  second 
theme  of  the  slow  movement  of  Schubert's  Fantasie,  Op.  78,  and  in  the 
slow  movement  of  his  sonata,  Op.  42. 

238.  1'ASSiNo-ToNBs:  there  are  Rood  illustration*  of  these  in  Schumann's  Kantnsie,  Op. 
17,  second  movement  (especially  in  measures  ,r>0-.r>7),  and  in  the  last  movement   <>l   Mendels- 
aohn's  Italian  Symphony. 

AUXILIARY  TONKH:  examples  of  these  may  be  found  in  Chopin's  study,  Op.  2.r>,  No.  0, 
in  the  last  movement  of  Schubert's  C  Major  Symphony,  and  in  the  last  movement  of  Beet- 
hoven's Sonata,  Op.  53. 

CilAN'civo  TONEH:  in  the  slow  movement  of  Beethoven's  Sonata.  Op.  2S.  and  in  Schu- 
bert's Impromptu,  Op.  142,  No.  1,  are  example."  ot  these  tones;  in  Chopin'ti  Study,  Op.  10, 
No.  4,  a  very  comprehensive  treatment  ot  them  may  Iw  found. 


222 


HARMONY 


_  XX         BACH:  Organ  fugue  in  G  minor 

-- *-»=  — t  r  i  ^- '  '  '   » 


APPOGG1ATURA8  : 


SCHUMANN:  Novelette,  Op.  21,  No.  6 
x 


WAGNEB:  "Die  Walkiire"  (Act  2) 


In  the  first  movement  of  Tschaikowski's  B  minor  symphony,  just  before  the  seconil 
theme  enters  in  B  major,  there  is  a  remarkable  exhibition  of  the  expressiveness  that  can  result 
from  the  appoggiatura.  See  also  the  finale  of  "Tristan  und  Isolde,"  which  is  full  of  inter- 
esting suspensions  and  appoggiatura.*. 


ANTICIPATION: 


HANDEL:  Chorus,  "His  yoke  Is  easy"  ("Messiah") 


HARMONY 


223 


GBIKG:  Song,  "Sol vejgs Lied" 
X  X 


BA  — 
" 


*  J 1 


** 


—      -    -    - 


FIOUKATION  : 


^r%*~< 
i    i 


BEETUOVEX:  String  quartet,  Op.  74 


The  following  is  an  unusual  example  of  a  melody  and  its  figuration  ROIIIK  on  simultane- 


ously. 


DICAIIMS:  D  major Symplio  ny 


j    *>.4  -  *  J  J  B'  ;  -  .  . 

:  J 


;i 


239.  All  music  comex  from  the  wale  ami  (ho  chord,  however  much  that  (art  may  l>e 
di-ir'ii^'  I  t'V  diatonic  or  chnimatic  ornamental  tones;  and  -r:il<-  passago*.  in  linn)  :in:il\-.-. 
are  found  to  have  chord*  for  their  harmonic  foundation.  The  thuiK  to  do  is  to  tirxt  reduce 
every  passage  (which  nece.Hsarily  in  ba-sed  on  .Mome  chords)  to  its  simplest  form.1 

1  A  helnful  little  l>fx>k  towards  understanding  this  question  is  Menjiunin  Cutter's  "Har- 
monic Analysis"  (Oliver  Dit.son  Co.). 


224 


HARMONY 


In  analysing  compositions,  the  student  is  no  longer  to  be  restricted  to  such  as  are  in 
four  real  parts.  It  is  well  to  study  other  music  also,  establishing  the  harmonic  outline,  and 
defining  the  chord  successions  clearly;  at  present,  songs  for  one  voice  with  piano  accompani- 
ment, and  the  simpler  kinds  of  piano  pieces,  will  be  of  use.  The  ornamental  tones  so  fre- 
quently present  must  not  obscure  understanding  of  the  chord  successions.  The  songs  of 
Schubert,  Schumann,  Mendelssohn,  l-'ranz.  and  others,  exist  in  cheap  editions,  as  do  the  piano 
works  of  Mozart,  Beethoven,  Chopin,  etc.  No  material  is  better  for  this  especial  study  than 
the  Mendelssohn  "Songs  without  Words,"  for  the  melody  is  always  simple  and  obvious,  the 
real  bass  of  every  chord  easily  found,  and  the  accompaniments  sufficiently  varied  but  not 
complex. 

For  an  exhaustive  study  of  part  writing,  and  especially  of  suspensions  and  of  chorda 
of  the  7th  used  in  the  freest  possible  manner,  the  student  is  referred  to  the  371  Vierstimmige 
Choralgesange  of  Bach  (Breitkopf  und  Hartel). 


CHAPTER  XLIV 

240.   EXERCISES    INTRODUCING    SUSPENSIONS,  APPOGGIATURAS,  PASSING- 
TONES,   AUXILIARY  TONES,   CHANGING   TONES,    AND   ANTICIPATION. 

OBSERVE  THAT  IN  SUSPENSIONS  THE  TONE  APPEARS  IN  THE  CHORD 
BEFORE,  BUT  DOES  NOT  DO  SO  IN  APPOGGIATURAS.  TlIE  ABOVE  DEVICES 
ARE  INDICATED  BY  THE  X,  THOUGH  THIS  IS  NOT  SHOWN  IN  ALL  CASES. 


XL  °"     P       & 

?      •    r    i      P                p 

^      r 

frh  '     r 

r                        '       r 

P      t 

\AJ  *•  • 

it          i            p 

' 

«J 

t_ 

l 
i           * 

V 

P           (3                m                                                                                     m 

»  u 

>T    p       « 

.__J                                f     B^ 

r^m               f  B* 

I(T\   r        r 

ZZSIII32         >d       >d                -  * 

V9        f 

-  /r    -  •     w  \t* 

a            J 

. 

i« 

i^ 

-   .... 

-43}  —    —  \t-^- 

^ 

*«!  '      *       * 

—m— 

^ 

m  i 

1   - 

A       ?h 

• 

] 

[nF. 
x              x 

X 

V     r         ^ 

1     p 

&      ~ 

1 

— 

>T               r 

P      0 

J 

^ 

U1              r 

h  —  P— 

—  • 

• 

1 

^  Ind. 

2. 

Oii          r^" 

I. 

—  - 

i 

* 

c. 

1-r          r*- 

'  1  1  —  ' 
x 

M  
X 

X 

L/fu.  0      ^^ 

-^    *          ~\ 

/L     »'• 

. 

m  • 

9    * 

p 

Im  "  Q         J 

* 

!     r 

1 

In  6. 


In  D. 


HARMONY 


225 


lu/Jf. 


In  D. 

x        x 


In  e.  In  G.     In  e. 

3.  x 


» 
In  D. 

>— *»i 


In  Afr- 


~^JT: 
'=-4: 


In  c. 


-In/. 


^=^^»^MH*> 

stiq  x     t3i=J          — **-  —  *~  -*-*--jLfe:  -: 


In  F- 


/? . .. .  ;*  •*  *  •  !*  *  ~v^  *^  I.  II 

Lffi_  r.  .- ;  •  "          •  - » -i          f  -   t--^—      :-  -.- 


In  c. 


Ill  If?. 


5. 


EH?       "fe  fi 


226 


x  x 


HARMONY 
x  x 


»    ff  ^  /\  /\  /\     | y\ 


t 


. 


I — ^t •- 

3=F 


9. 


In  pf.        In  Ft. 


^n 


InB. 


In  cj. 


InB. 


r 


HARMONY 


227 


tee 


luF. 


CHAPTER   XLV 

MODULATION 

241.  A  musical  composition  of  any  length  will  Ix*  tedious  if  it  remains 
throughout  in  the  same  key;  some  changes  will  be  felt  desirable.  \Ve 
therefore  find  that  such  are  frequent  in  modern  music;1  at  each  time 
that  one  occurs  a  new  tone  is  to  be  taken  as  the  tonic  for  the  time  l>eiii£, 

«  The  music  of  Bach  is  so  mo<lern  in  the  true  »oni«  of  the  wonl.  that  this  term  must  tx- 
understood  to  cover  the  perio<i  of  the  last  two  hundred  years  at  least :  modern  mu.Hic  is  l>y  no 
means  only  that  produced  yesterday,  and  indeed  some  oi  the  latter  is  already  antiquated 
to-day. 


228 


HARMONY 


at  the  conclusion  a  return  being  nearly  always  made  to  the  original 
key.  The  mere  succession  of  different  keys  does  not  of  itself  constitute  modula- 
tion. For  the  definition  of  that  term,  and  a  few  of  the  simplest  ex- 
amples, cf.  §  108. 

Modulation  may  be  so  fleeting  as  to  seem  barely  to  deserve  the  name 
(for  the  general  tonality  of  the  following,  e.g.  is  not  affected  by  the  chromatic 
alterations  of  the  chords) ; 


or  may  be  of  a  settled  character.  In  the  latter  case,  it  must  not  only 
take  us  definitely  into  a  new  key,  but  should  keep  us  in  that  key  long 
enough  to  make  us  feel  that  a  return  to  the  former  key,  or  a  change  to 
another  new  key,  will  demand  another  distinct  modulation.  / 

242.    In  determining  our  key,  we  should  not  be  misled  by  looking  at  one  chord  alone, 
but  must  consider  also  the  chords  preceding  and  following.     Take  this  chord,  for  instance: 


the  following  examples  show  that,  ot  itself,  it  does  not  fix  the  key  in  which  we  are. 

X  X 

J-JU.LJ; 


T^UaJ 


mi 


HARMOXY 


229 


A  chromatically  altered  tone  must  not  confuse  us. 


A  MODULATION  CAN  BE  PRODUCED  ONLY  BY  INTRODUCING  ONE  OR  MORE 
TONES  FOREIGN  TO  THE  KEY  IN  WHICH  WE  ARE,  AND  BELONGING  TO  THE 
KEY  TO  WHICH  WE  ARE  GOING. 


243.  It  is  of  the  utmost  importance  to  understand  at  every  point,  u-here  a  change  is  made, 
just  what  signature  and  what  accidentals,  if  any,  are  indicated  or  implied.  It  is  especially  help- 
ful to  know  thoroughly  the  signatures  and  accidentals  (the  latter  resulting  from  leading- 
tones)  of  the  minor  keys. 


a       e         b  f$          cj  gf  df 

The  leading  tones  are  enclosed  in  (  ). 


The  student  is  advised  to  find  what  are  the  keys  of  the  following  scales. 


230 


HARMONY 

=^=-^fe 


mi 


Write  the  original  chords  of  which  the  following  are  inversions,  and  find  out  in  what 
key,  or  keys,  each  chord  can  occur. 
(See  the  note  on  page  72.) 


I       »> 


244.  It  is  a  helpful  statement  that  "the  nearest  related  keys  to  any 
major  key  are  its  dominant  and  sub-dominant,  and  the  relative  minors  of 
these  three  keys;  the  nearest  related  keys  to  any  minor  key  are  its  domi- 
nant and  sub-dominant  minors,  and  the  relative  majors  of  these  three 
keys."  (Prout.) 

It  must  be  understood  that  each  of  the  modulations  that  follow  is 
given  as  showing  one  of  various  ways;  they  are  all  made  by  the  plainest 
and  most  definite  means  —  by  introducing  the  new  tones  foreign  to  the 
old  keys,  and  concluding  with  an  authentic  cadence  (generally  including 
a  6-4  chord)  in  the  new  key.  Refer  to  the  modulations  given  in  §  109. 


Ctoe. 


HARMONY 


231 


Ctod. 


We  can  also  modulate  from  C  to  G  (I  to  V)  and  then  to  e,  the  relative  minor  of  G;  from 
C  to  F  (I  to  IV)  and  then  to  d,  the  relative  minor  of  F. 

The  diminished  7th,  and  the  augmented  6,  6-5,  and  6-4-3  chords  are  very  useful  (see 
later  the  modulations  C  major  to  Eb  major,  a  minor  and  g  minor).1 

245.  Taking  C  for  our  tonic  major,  we  can  also  modulate  as  follows:  to  D  major  by 
going  to  G,  and  then,  taking  G  as  a  new  tonic,  modulating  to  D:  to  A  major,  by  passing  through 
d  minor. 

To  E  major,  by  a  modulation  to  a  minor  and  then  to  the  dominant  of  the  latter  (E); 


In  this  last  modulation  we  notice  the  key-relationship  of  tonic  and  mediant.  The  term 
mediant  relationship  is  now  as  well  recognized  as  that  of  dominant  relationship.  This  is  also 
apparent  in  the  keyrelationship  of  movements  of  symphonies,  cf.  Raff's  "  1-enore"  symphony, 
the  movements  of  winch  are  respectively  in  the  keys  of  K  major,  A  flat  major  (enharmonic), 
C  major,  and  e  minor,  with  a  final  coda  in  K  major. 

Compare,  later,  the  modulations  to  107  and  Ab  major; 
to  B  major  or  6  minor  through  a  passing  chord  ol  e  minor; 


I  The  enharmonic  use  of  augmented  and  dominant  7th  chords  a«  a  mean?  of  modula- 
tion was  spoken  of  in  §  202;  see  al.so  §§  112,  113,  121,  t.ij. 


ff 

*- 


, 

._    J- 


The  Liszt  song  referre<l  to  later  in  thi-i  chapter  is  an  excellent  illustration. 


232 


HARMONY 


to  F$  major  only  by  passing  through  other  keys  (e.g.  e  and  6  minor); 

to  Bb  major  by  going  to  F  major,  and  then,  taking  the  latter  a-  a  new  tonic,  modulating  in 

the  same  way  to  Bb  major; 

to  lib  major  (the  minor  3d  above,  and  the  relative  major  of  the  tonic  minor  of  C); 


to  Ab  major  (the  major  3d  below)  through  /  minor; 
to  Db  major,  also  through  /  minor; 

^       X          .     X 


to  a  minor,  by  means  of  an  augmented  chord  (see  page  85); 


to  g  minor; 


to  c  minor  by  means  of  the  dominant  7th,  common  to  both  keys  (p.  72): 

to  /  minor  in  the  same  way  as  to  F  major;  to  fcb  minor,  through  Db  major.  There  is  so  little 
logical  connection  between  C  major  and  the  keys  of  /$,  cf,  g$,  and  d$,  (eb)  minor  that  a  mod- 
ulation to  any  of  them  can  be  effected  only  in  a  roundabout  manner. 

246.    Taking  a  as  our  tonic  minor  (for  the  modulation  to  its  relative  major,  r/.  §  109) 
we  can  modulate: 
to  its  dominant,  ~E  (major  or  minor); 


HARMONY 


233 


to  its  sub-dominant  d  (minor) ; 


X  x 


to  F  major,  its  sub-mediant; 


to  G  major; 


to  D  major  (through  G  major); 

to  A  major  in  the  smoothest  way  through  d  minor;1  to  B  major  (or  6  minor)  its  gupertonic, 

through  e  minor; 

to  Bb  major  through  F  major; 

to  Efr,  Ab,  Dfr,  Gfr  (or  Ff)  major  only  through  previous  modulations; 

to  ft  minor  through  6  minor; 

to  <•£  and  g$  minor  through  previous  modulations; 

to  g  minor; 

X 


•  The  old  custom  of  ending  a  minor  piece  with*  major  3d  (Tierce  de  1'icardic.  §65), 
continued  well  into  modern  mimic,  for  that  ending  is  e.g.  often  found  in  Bach:  the  alternative 
was  a  unison  or  a  chord  with  a  5th,  but  without  a  3d  (r/.  the  e*.«ny  on  "  Harmony  "  in  "  Grove'* 
Dictionary").  In  Horatio  Parker's  "flora  Novis-tima."  the  following  closes  of  the  latter 
Bort  are  made  in  the  unaccompanied  chorus  "I'rb*  Syon  Umca"  (in  this  case  the  chorus  being 
in  a  major  key). 


234 


HARMONY 


to  c  minor  through  g  minor; 

to  /  minor  best  through  F  major  and  lh  minor; 

to  fJ  (dj)  minor  through  previous  modulations. 

The  examples  of  modulation  given  in  this  chapter  are  purposely  of  a  simple  and  con- 
ventional sort;  to  make  a  comprehensive  statement  of  more  subtle  methods  would  take  too 
much  space.  For  the  very  short  passing  modulations  that  are  so  frequent  now-a-days,  we 
by  no  moans  necessarily  expect  even  the  dominant  chord  of  the  new  key,  still  less  the  dominant 
7th  or  the  6-4  chord.  It  is  occasionally  the  case  that  a  new  key  is  proceeded  to  without  any 
modulation,  or  intermediate  step,  e.g. 


SCHUBERT:  Sonata,  Op.  53  (Scherzo) 


In  Schubert  we  also  note  a  fondness  for  unexpected  alternations  of  tonic  major  and  minor 
(Unfinished  Symphony,  slow  movement). 


CHANGES   OF   KEY   WITHOUT   MODULATION 

247.  Two  of  such  changes  are  well  known  as  being  exceedingly  effective  —  from  a 
major  key  to  a  new  tonic  major  downward  by  a  major  3d,  and  to  a  new  tonic  major  or  minor 
upward  by  a  minor  3d  (see  the  preceding  example  by  Schubert). 

A  notable  instance  of  the  former  is  in  the  last  movement  of  Beethoven's  9th  Symphony, 
just  before  the  tenor  solo;  an  example  of  the  second  change  may  be  found  in  the  last  movement 
of  the  1st  Symphony  of  Brahms  (page  92  of  the  score),  the  second  chord  in  the  latter  being 
in  a  minor  key. 


Observe  the  enharmonic  change  at  the  X. 

248.   More  subtle  changes  are  seen  in  the  following,  in  which  chords  between  are  elided; 
the  effect  would  be  an  ordinary  one  were  the  elided  chords  sounded. 


HARMONY 

WAGNER:  "Das  Rheingold" 


235 


WAGNER:  "Parsifal'' 


(With  the  elided  chords.) 


249.  In  these  last  examples  also  we  have  enharmonic  changes.  Knharmonic  notation 
results  from  the  fact  that  we  can  write  notes  as  sharps.  Hats,  naturals,  double  sharps,  or  double 
flats,  as  the  case  may  be. 


This  notation  is  used  chiefly  for  convenience,  and  often  to  avoid  the  use  of  too  many  or 
confusing  accidentals;  a  beautiful  enharmonic  change  may  be  found  in  the  slow  movement  ot 
Beethoven's  7th  Symphony;  see  the  last  page  of  Liszt's  I)  Flat  Ktude  (No.  3  of  "3  Etudes  de 
Concert");  also  Elsa's  scene  in  the  first  act  of  "Lohengrin."  (Scene  2,  measures  9-13.) 


ELGAR:  "Dream  of  Gcron tins' 


>4_      **4- 


h 


T3*~ 


J_   -rioj-r 

"          *'~^        »"' 


^S- 


236 


HARMONY 


WAONER:  "Siegfried,"  Act  3 


Mm       mi 


Hit  A  ii  MS:  Ballade,  Op.  10,  No.  2. 


15s 


WAGNER    "Parsifal* 


Observe  in  the  following  the  differing  notations  in  the  voice  and  accompaniment,  for 
ease  in  reading;  also  the  perfectly  good  consecutive  5ths  (see  page  26). 


VOICE. 


FRANCK:  "Les  Beatitudes" 
X         x 


=3=5 


=• 


r 


^p=t 


Augmented  chords  and  dominant  7th  chords  may  be  interchangeable  through  enhar- 
monic writing. 

LISZT:  Song,  "Kennst  Dudas  Land?" 

£=t=± 


HARMONY 


237 


250.   The  variety  of  enharmonic  changes  is  endless,  and  the  preceding  gives  the  merest 
hint  of  what  can  be  done  in  this  direction. 

In  fact,  the  subjects  of  modulation  and  of  change  of  key  without  modulation  cannot 
be  learned  from  a  book;  individual  investigation  through  much  reading  of  music,  and  experi- 
menting, are  the  only  ways  by  which  one  can  hope  to  become  acquainted  with  the  possibilities. 

It  is  advised  that,  the  following  modulations  be  written  out,  and  also  improvised  at  an 
instrument. 

G  to  D;  Dtoe;  Ab  to  c;  F  to  e;  Bb  to  d;  6toG;  etod;  /  to  Db;  Ff  toe;  I)b  to /$;  K 
to  F;  g  to  l^T;  B  to  G;  #  to  G;  eb  to  <J7;  Ab  to  (ft;  Kb  to  Cb;  cj  to  A;/  to  Ab;  B  to  0$. 


CHAPTER  XLVI 

EXERCISES    IN    MODULATION 

251.    MARK  the  modulations  (C,a,  etc.):  if  is  expected  that  suspensions  and  ornamental 
tones  will  be  u*ed.     I'assing-tone.s  are  indicated  by  slurs. 


L.     (Chant) 

IL     Uf 


:3T^f  *-|^fe -&4*d3B3E  V   H 
-  r.__Lp  i_Ep  3~  :__^L«^1^  1:1 

2.     (Hymn-tune) 

9th 


3.     (Hy  ran -tune) 

'    ' 


238 


HARMONY 


Allegretto. 


i       I         |       i        j — 


^ 
pFffe 


£E=  zz^^lizprzflpzpig-fcq: »-^       — 


6.     (Hymn-tuue) 


=K=: 


6+ 
5 


; 


"~~ 


6. 


7.     (Hymn-tune) 


^_IP=gzg--g=g-g- 


fd: 


=1= 


HARMONY 


239 


i  —  (9-       -  M      -                    f3  '                                   e?         h                   i_        "r3          • 

L/    /<••_•                             •  •                   •           I-'.          /^                       k_ 

Fr^h 

i  f  —  '  !  • 

CHAPTER  XLVII 

CROSS   RELATION    (FALSE    RELATION) 

252.  WHEN  a  tone  of  one  chord  occurs  in  another  chord,  in  a  different 
voice,  chromatically  altered,  and  so  soon  that  the  effect  of  the  one  tone 
has  not  passed  from  the  mind  before  the  other  appears  to  contradict  it 
with  its  chromatic  alteration,  we  have  a  CROSS  RELATION. ' 

1  The  following  cannot  IHS  properly  called  a  cross  relation,  for  the  A3  is  an  appoRKui- 
turi,  not  affecting  the  tonality;  s:>me  theorists  include  in  the  definition  the  simultaneous 
appearance  of  the  altered  and  unaltered  tone  in  the  same  chord. 

X 


In  fact  the  cross  relations  produced  by  the  appoKKiatunis  in  the  next  illustration  do  not 
result  in  a  bad  effect.  

v<$~*  I-"  i*-*  •  -"i-  *  *  *~*  ..i  ^i 

L?— -iliij"  *TJ>  *  *  *^  *  >  .'I  - 

('/.  Schumann's  Amliuito  and  variation"  for  two  pianofortes. 


HARMONY 


It  is  difficult  to  lay  down  definite  rules  as  to  usage;  the  feeling  of 
musicians  has  become  so  modified  of  late  years  that  we  may  practically 
say  that  no  cross  relation  is  forbidden  that  sounds  tolerably  well. 

263.  The  harshest  form  of  it  is  when  the  3d  in  a  tonic  triad  is  major 
and  minor  in  different  voices  in  two  successive  chords,  the  effect  not  being 
altered  by  the  interposition  of  a  passing-tone  or  of  another  chord: 


for  we  almost  get  the  feeling  that  two  keys  are  used  at  the  same  time. 


SCHUBERT  :  Impromptu,  Op.  90,  No.  1 


BRAHMS:  Symphony  in  F  major 
X 


The  capricious  shifting  between  tonic  major  and  minor  ia  a  characteristic  ot  Schubert 
(cf.  his  song  "  Rosamonde");  in  this  illustration  the  effect  is  softened  by  the  fact  that  Eb 
is  in  the  lower  voice  also,  the  change  to  K3  taking  place  in  that  voice,  §  254) ;  Brahms  simply 
had  two  vital  themes,  which  he  intended  to  work  together  without  regard  to  a  temporary 
roughness. 


254.  The  result  is  generally  good  when  both  the  original  and  the  altered 
tone  occur  in  the  same  voice,  as  well  as  the  altered  tone  in  the  other  voice 
also  (o),  or  (§  138)  when  the  chromatically  changed  tone  is  a  new  lead- 
ing-tone in  a  modulation  (6).  There  are  many  cases  where  a  cross  rela- 
tion sounds  better  than  it  looks  upon  paper ;  we  sometimes,  however,  may 
prefer  to  avoid  the  effect  by  a  change  in  one  of  the  voices,  for  the  sake 
of  the  slight  improvement  (c). 


(c)  Better. 


LISZT:  Song,  "Die  Lorelei" 
X 


BACH:  "Well-Tempered  Clavichord  "  Vol.  I,  Fugue  No.  2 

X 


CHAPTER  XLVIII 


8UOOKSTIONS   TO    AID    IN    RKVIKWIN'O 

265.  THE  stiulent  must  bear  in  mind  that  it  is  not  enotiKh  simply  to  write  down  the 
exercises,  even  if  that  t>e  done  correctly.  They  must  be  li.itcnpd  lo,  and  in  playing  thorn  over 
the  ear  must  try  to  disentanRle  the  separate  parts  and  to  hear  the  individual  voices.  Writing 
exercises  from  figured  basses  serves  in  showing  us  how  to  think  of  chords  and  to  notice  the 
logical  ways  in  which  they  succeed  each  other;  the  ability  to  hnnnomzr  soprano  melodies  and 
basses,  without  the  aid  of  figures,  is  of  utmost  consequence.  'l"he  student  in  also  strongly 
advised  to  compose,  from  the  very  beginning  of  this  review,  some  original  b&wes  and  melo- 
dies to  be  harmonized. 


242 


HARMONY 


888.  The  exercises  are  to  be  written  with  the  voices  on  four  separate  staves;  the  C  clefs 
are  to  be  used  to  some  extent.  The  exercises  are  also  to  be  this  time  transposed  a  tone  or 
semitone  higher  or  lower,  without  exception.  Besides  playing  them  over,  the  student  i-  ad- 
vised to  read  them  at  the  piano  from  the  bass  or  soprano  given,  even  though  it  is  at  first  dim- 
cult  to  keep  the  progressions  of  the  separate  voices  clearly  in  one's  bead. 

Do  not  be  mechanical;  endeavor  to  be  musical;  aim  at  having  an  attractive  and  singable 
soprano  and  a  varied  and  strong  bass,'  not  neglecting  good  voice-leading  in  the  alto  and  tenor; 
do  not  be  satisfied  with  the  first  writing  of  an  exercise,  unless  convinced  that  you  cannot 
improve  it.-  Open  or  close  position  is  to  be  used  as  may  seem  best.  \Ve  often  change  from 
one  to  the  other  several  times  in  one  exercise  (pp.  42,  54,  137)  ;  this  is  not  only  done  for  variety, 
but  may  be  necessary  in  order  to  avoid  consecutive  8ves  and  5ths.  On  the  above  points 
individual  study  and  analysis  of  good  choruses  and  part  songs  will  be  more  helpful  than  advice. 

Contrary  motion  is  often  more  symmetrical  than  similar  motion,  where  either  is  correct ; 
contrary  motion  is  generally  to  be  preferred  to  similar  motion,  in  approaching  a  dissonance. 

As  for  spacing  of  the  voices,  it  is  safe  to  say  that  the  limit  of  an  8ve  should  seldom  he 
exceeded  between  soprano  and  alto,  or  alto  and  tenor;  the  bass  may  be  even  two  8ves  distant 
from  the  tenor. 

257.  With  TRIADS  IN  MAJOR  KEYS  think  of  these  two  things,  viz.  consecutive  8ves 
and  Sths,2  and  the  leading-tone  (p.  29).     With  triads  in  major  keys  we  meet  with  the  interval 
of  the  augmented  4th,  and  IN  MINOR  KEYS  with  those  of  the  augmented  2d  and  4th,  such  skips 
to  be  at  present  avoided  as  unvocal  (pp.  39,  41,  42). 

With  BOTH  MAJOR  AND  MINOR  TRIADS  consider  the  question  of  doubling  (generally  the 
root),  and  the  progressions  from  the  second  to  the  fifth  and  the  fifth  to  the  sixth  triads;  do 
not  double  the  leading-tone  except  in  sequences. 

258.  With  CHORDS  OF  THE  GTH  we  must  ask  when  the  bass  is  to  be  doubled,  a  thing  as 
to  which  only  very  general  directions  can  be  given  (n.  57).     THE  6-4  CHORD  is  discussed  at 
page  57;  compare  its  use  as  a  cadential  and  as  a  passing  chord. 

259.  A  statement  of  the  usual  treatment  of  the  DOMINANT  7ra  CHORD  is  at  page  71,* 
and  of  its  inversions  at  page  83;  of  the  irregular  resolutions  at  pages  93  and  105.     As  either 
root  or  7th  may  be  prolonged  into  the  next  chord,  ascend,  or  descend,  there  is  much  detail. 
Some  SIMPLE  MODULATIONS  are  spoken  of  at  page  85;  a  statement  of  PASSING-TONES  will  be 
found  at  pages  77  and  138,  and  of  AUXILIARY  TONES  at  page  78.     These  ornamental  tones 
are  to  be  used  freely,  but  with  discretion. 

The  dominant  7th  has  been  used,  from  a  purely  musical  point  of  view,  too  much  in  the 
exercises  of  this  book,  the  intention  being  to  get  the  student  accustomed  to  the  various  ways 
in  which  it  appears.  The  authentic  cadence  is  stronger  when  the  dominant  triad  is  employed 
without  the  7th.  In  reviewing,  consider  when  that  change  is  to  be  preferred,  for  variety  if 
for  no  other  reason. 

1  See  page  63.  A  bass  should  move  largely  step-wise,  although  we  may  have  even  several 
moderate  skips  in  succession;  diminished  skips  are  often  good,  augmented  ones  seldom;  when 
a  chord  is  repeated,  it  is  sometimes  well  to  have  the  bass  skip  an  octave  at  the  repetition;  it 
is  best  not  to  return  to  the  tonic  unnecessarily  often,  as  that  produces  monotony;  two  skips 
of  a  4th  or  5th  in  succession  are  generally  to  be  avoided;  cf.  Spalding's  "Tonal  Counter- 
point," pp.  24-38. 

*  An  allowable  license  is  that  soprano  and  bass  may  sometimes  move  in  consecutive 
8ves  in  contrary  motion,  when  the  dominant  is  followed  by  the  tonic  triad  (p.  74,  top  line). 

8  A  unison  followed  by  an  8ve,  or  8v»  followed  by  unison,  produces  the  effect  of  con- 
secutive 8ves,  and  is  to  be  avoided.  A  unison  followed  by  a  7th  is  equally  bad,  and  a  change 
in  the  leading  of  one  of  the  other  voices  will  remedy  this  defect,  e.g. 


should  be 
changed  to 


HARMONY  243 

With  the  INVERSIONS  OF  THE  DOMINANT  VTH  chord  we  meet  with  the  fact  that  consecu- 
tive 5th3  are  allowed,  when  one  or  both  are  not  perfect  (pp.  106,  108). 

With  the  MODULATIONS  occurring  in  exercises  always  look  tirst  of  all  for  the  leading 
tone  of  the  new  key;  continue  to  transpose  every  exercise  written. 

260.  CHORDS  OF  THE  ?TH  ON  THE  LEADING-TONE  (pp.  114,  120);  we  again  find  both  root 
and  7th  with  a  variety  of  less  usual  resolutions;  observe  the  ambiguity  of  the  diminished  7th 
chords. 

261.  CHORDS  OF  THE  7TH  ON  OTHER  DEGREES  THAN  V  AND  vn°;  compare  the  strict  rules 
for  preparation  (p.  132)  with  the  hints  as  to  free  treatment  (p.  128);  remember  that  prepara- 
tion is  often  desirable,  even  when  unnecessary;  there  are  many  irregular  resolutions.   Generally 
speaking,  we  should  try  for  a  smooth  leading  of  the  voices.     With  SUCCESSIVE  CHORDS  OF 
THE  "TH  in  root  position,  be  careful  that  the  arrangement  of  the  voices  is  good  at  starting  (p. 
136),  as  every  alternate  chord  will  be  incomplete.      INVERSIONS  OF  SECONDARY  7TH  CHORDS, 
with  their  various  resolutions,  are  described  on  page  142. 

262.  It  has  been  said  that  passing  and  auxiliary  tones  should  be  used  even  in  the  simple 
triad  exercises;  with  the  secondary  7ths  (if  not  before)  introduce  SUSPENSIONS  and  APPOGGI- 
ATURAS  occasionally  (p.  153).      To  have  theselatter.it  will  be  necessary  to  change  the  figured 
bass  or  the  soprano  melody  given;  the  exercises  may  also  be  altered  to  admit  of  the  introduc- 
tion of  occasional  CHROMATICALLY    ALTERED    CHORDS,  AUGMENTED  CHORDS,  and,  very  spar- 
ingly, Of  CHORDS  OF  THE  &TH. 

263.  With  the  CHORD  OF  THE  QTH  (p.  152)  independent  chords  end,  for  practical  pur- 
poses.    In  the  discussion  of  CHORDS  OF  THE  HTH  AND  13TH,  however,  it  is  recognized  that 
examples  such  as  those  from  "  Die  Meistersinger"  forbid  our  dismissal  of  the  claims  of  such 
chords  to  be  considered  independent;  but  the  question  cannot  as  yet   be  considered  settled. 

The  fundamental  points  regarding  SUSPENSIONS  are  plain.  The  suspended  tone  and 
the  tone  of  resolution  must  be  in  the  same  voice;  the  tone  of  preparation  is  usually  at  least  as 
long  as  that  of  suspension,  and  the  tone  of  suspension  is  generally  accented;  no  progression 
which  would  be  incorrect  without  a  suspension  is  justified  by  its  presence;  if  the  tone  of  reso- 
lution is  anticipated  in  another  voice  also,  the  two  tones  must  not  be  less  than  an  8ve  apart; 
there  is  much  detail,  (p.  199.) 

264.  It  will  be  of  advantage  to  again  write  some  EXERCISES  WITH  THREE  VOICES;  there 
is  nothing  that  makes  the  harmonic  structure  so  clear  t6  the  mind  (pp.  43,  65,  80). 

Finally  —  listen  with  eye  and  with  ear  to  what  you  write. 

If  fresh  exercises  are  desired  for  review  work,  the  additional  exercises  to  Emery's  "  Har- 
mony" will  be  useful. 


CHAPTER  XLIX 

THE    PEDAL    (PEDAL    POINT,    ORGAN    POINT,    POINT    D' 

265.  THE  PEDAL  is  deh'nec'  as  the  oustaining  of  a  tone  or  t  >nes  in  one 
or  more  voices,  while  the  other  voices  move  through  a  succession  of  har- 
monies, some  of  which  are  foreign  to  the  tone  or  tones  forming  the  pe<lal. 

The  fact  that  a  tone  is  sustained  through  harmonies,  a  few  of  which 
are  slightly  different,  does  not  of  itself  always  constitute  a  pedal;  e.g.  the 
introduction  to  "Das  Hheingold"  is  not  a  pedal,  in  the  true  sense  of  the 
term.  In  one  there  must  be  harmonies  frequently  present  that  are  entirely 
foreign  to  the  sustained  tone,  i.e.  dissonant  from  it. 


244 


HARMONY 


266.  The  rules  given  by  the  older  theorists  differ  so  much  from  the 
practice  of  modern  composers  that  a  statement  about  the  pedal,  as  it  is 
used  to-day,  must  be  modified  from  that  formerly  given. 

The  important  facts  are  these:  (a)  the  pedal  tone  is  practically  always 
dominant  or  tonic;  (6)  chords  of  which  the  pedal  can  be  considered  as 
forming  an  integral  part  must  alternate  with  foreign  harmonies  sufficiently 
often  to  produce  a  good  logical  effect;  (c)  the  pedal  tone  is  generally  in  the 
bass,  but  may  occur  in  any  of  the  other  voices;  (rf)  it  is  best  for  it  to  har- 
monize with  the  chords  that  begin  and  end  the  pedal,  although  there  are 
exceptions  to  this. 

267.  We  find  the  pedal  on  the  dominant  in  the  bass  used  very  often 
to  introduce  the  third  portion,  or  at  the  very  end  of  a  sonata  movement  or 
of  a  fugue:  cf.  Beethoven,  Op.  13,  first  movement;  Op.  22,  first  movement; 
Op.  27,  No.  2,  last  movement;  Op.  53,  first  movement.1     In  the  following 
is  shown  a  pedal  on  the  dominant,  covering  several  octaves. 

BEETHOVEK:  Sonata,  Op.  31,  No.  2 


268.  The  pedal  in  the  bass  on  the  tonic  is  also  very  much  used. 
Remarkable  examples  of  it  may  be  found  in  the  prelude  to  the  great  a 
minor  organ  fugue  of  Bach;  at  the  end  of  the  c$  minor  fugue  in  Vol.  I  of 
the  "  Well-tempered  Clavichord,"  and  most  striking  of  all  —  the  introduction 
of  the  c  minor  symphony  of  Brahms.  A  double  pedal  in  the  bass,  on  tonic 
and  dominant,  has  been  employed ;  c/.  Beethoven's  "  Pastoral  Symphony," 

1  The  result  is  a  pedal,  even  when  the  one  i'  ..ot  sustained,  but  (a)  interrupted  by  rests 
(6)  ornamented,  as  by  an  auxiliary  tone,  or  (c)  made  part  of  a  figure:  (a)  first  movement  of 
Beethoven,  Op.  Ill;  (6)  last  movement  of  Beethoven's  7th  Symphony, 


I         I     I    i 

-*    w     -*- 


etc.;  (c)  first  movement  of  Beethoven,  Op.  53. 


HARMONY 


245 


"he  waltz  in  the  3d  act  of  "  Die  Meistersinger/'  the  first  movement  of  Brahms' 
F  Major  Symphony;  attempts  have  even  been  made  at  constructing  a 
triple  pedal,  but  with  no  great  success. 

269.  When  the  pedal  is  in  the  soprano  it  is  called  an  inverted  pedal. 
Excellent  instances  of  this  are  in  Mendelssohn's  Overture,  "  Meeresstille 
und  Gliickliche  Fahrt,"  and  in  the  following: 

WAGNEH:  "Flying  Dutchman"  Overture 


as  well  as  in  Borodin's  "Eine  Steppenskizze  aus  Mittel-Asien,"  in  which 

8va 

9- 

i]  is  sustained  for  ninety  measures. 

270.    As  an  illustration  of  the  pedal  in  inner  voices,  the  following  is 
given: 

GIUEO:  Pianoforte  Concerto 

•       »     •        •  »       •     •        »  •      •     •        •  •       »     •        * 

•* —     H —  -i — •        •• —  ^ —     - —  -t—        -i —  -t —      -f —        -t —  -* —      -»--  -c~ ~        -t — • 

i~  -. , . — - — . -] 1 t rv~* ' — ~* 1 — \ — ' ' *~  —  ' n 

p    •  • -=3K-gj^y.J.-g-fc^i=»— EJ:Z«^=)K-,IK — fc_ Qryi-jEriK  -  >tzj 
-  -t— F^PSp-f- 1- r^T-  m—p F=fy-; r-r—  t— H 


*2: 


zzrbr^L 


271.  In  the  introduction  to  "Die  Walkiire,"  and  in  the  chorus,  "Hut  the  riKhteou* 
souls  are  in  the  hand.H  of  tiod,"  from  the  IlrahmH  Hequiom,  will  he  found  two  of  HIP  most  re- 
markable pedals  in  existence.  The  student  is  referred  to  the  following  as  well  worth  exam- 
ination: 

Txchaikowaki,  first  movement  of  6th  Symphony;  Hcrlioz,  "Bullet  des  Sylphes,"  from 
"La  Damnation  de  Faust";  Hcethoven,  the  cndniK  ot  the  Srheno  of  the  fith  Sym|>hony; 
Mrahms,  last  movement  of  /  minor  Sonata,  Op.  .5;  Beethoven,  introduction  of  Sonata.  Op. 
Ill,  for  a  pedal  in  an  inner  voice;  Schumann,  Kth  Nuvolelto;  Beethoven,  the  beginning  ot  Op. 
28;  Schumann,  finale  of  "Variations  Symphoniques,"  <  )p.  13;  Schumann,  fuRue  on  H-A-O-H, 
Op.  00,  No.  1;  Beothoven,  first  movement  of  string  quartet  Op.  M),  No.  1,  for  a  pedal  in  an 
inner  voice;  the  introduction  of  Mendelssohn's  2d  <  )rgan  Sonata,  tor  the  «ame;  Hrnhins,  Inter- 
mezzo, Op.  117,  No.  1,  for  a  pednl  in  the  soprano;  the  song  of  Cornelius.  "Km  Ton,"  for  the 
same;  Beethoven,  the  last  movement  of  Sonata,  Op.  l()fl,  for  pedaU  in  different  voices;  Men- 
delssohn's Variations,  Op.  82,  for  modulation  alxive  a  dominant  pedal  in  the  hass.  As  an 
example  of  a  pedal  simultaneously  above  and  l>elow  the  changing  harmonies,  the  end  of  the 
hlow  movement  of  Beethoven's  Sonata,  Op.  10,  No.  3. 


246 


HARMONY 


272.  Although  pedals  on  other  degrees  of  the  scale  are  rare,  they  some- 
times occur.  Two  good  illustrations  are  in  the  second  movement  of  Schu- 
mann's E  flat  Symphony  (on  the  mediant),  and  in  the  following: 


TSCHAIKOWSKI:  5th  Symphony 


273.  It  is  of  great  consequence  to  remember  this,  that  the  voice  next 
above  the  pedal  in  the  bass  is  generally  to  be  regarded  as  the  real  bass, 
chord  progressions  being  made  independently  of  the  pedal  tones;  also, 
although  it  is  not  to  be  stated  as  a  fixed  rule,  it  is  well  to  aim  at  having 
approximately  every  alternate  chord  such  that  the  pedal  tone  can  form  a 
part  of  it.     No  modulation  that  sounds  well  is  forbidden,  but  extravagance 
in  that  direction  easily  results  in  harshness. 

274.  The  old  rule  that  tne  pedal  tone  must  be  either  tonic  or  dominant  seems  to  indi- 
cate the  Drone-bass  as  its  origin.   The  Drone,  in  which  the  tonic  is  sustained  as  an  accompany- 
ing tone  through  a  whole  piece  or  large  portion  of  a  piece,  is  considered  by  some  as  the  oldest 
form  of  harmony.     We  hear  it  to-day  from  the  Scottish  bagpipes;  two  examples  follow.      It 
will  be  observed  that  in  these  the  nature  of  the  piano  does  not  permit  such  a  tone  to  be  indefi- 
nitely sustained,  but  that  it  must  be  repeated  from  time  to  time. 

BACH:  Gavotte  in  G  minor 
(Musette) 


tr 


BACH:  Gavotte  in  D  minor 
(Musette) 


e=* 


etc. 


The  Musette  was  an  instrument  of  the  bagpipe  family;  the  second  part  (Trio)  of  the 
Gavotte  was  sometimes  written  to  imitate  the  effect  of  that  instrument  and  was  given  that 
Dame.  A  modern  example  is  in  the  Gavotte  of  D' Albert's  Suite,  Op.  1,  for  piano. 

EXERCISES   WITH   A   PEDAL, 

275.  Add  the  inner  parts;  aim  at  having  a  variety  of  chords;  it  is  intended  that  there 
shall  be  chromatically  changed  chords,  augmented  chords,  suspensions,  appoggiaturas,  etc. 


HARMONY 


247 


1.    Moderate 


2.     Con  moto 


ritard 


^J_J    I" 


3.    Andante 


I  I 


=  '-•  -     --     ?lff 


4.       Allffjrrtfn 


^rf  •        :  > 


248 


HARMONY 


t 


•*=z 


"<r 


I 


cJ 

±pi^ntirt 

1  Tt-  

V 

4=t 

p-l-  
:e=iV  — 

:-A 

6.     Maestoso 


^^^==.0;,    I  p- 
**^r^      l   TII_ 


JP^?FP=^^^^ 

23  i  

J    ^"^'    ^ 

r  -^ 

M  =r  r  i  rj  —  F==f-r?'    *r  ^ 

-I        I 


7. 


(Add  the  Alto) 


HARMOXY 


249 


CHAPTER  L 

THE   OLD   MODES 

276.  THE  ancient  Greeks  used  in  their  music  a  number  of  MODES,  as  they  are  called ;  as 
no  sharps  or  tiats  were  employed,  the  simplest  way  to  get  an  understanding  ot  their  effect  is 
to  play  scales  on  the  white  keys  of  the  piano,  taking  the  different  tones,  C,  D,  K,  F,  G,  A,  B,  as 
the  starting,  or  principal  tones.  The  distribution  of  tones  and  semitones  will  not  be  the 
same  as  with  our  modern  scales  (with  the  exception  of  the  mode  beginning  on  C)  and  the  use 
of  the  words  key,  keynote,  and  scale  is  inappropriate  in  this  connection. 

According  to  tradition,  four  of  these  modes  were  adopted  by  St.  Ambrose  at  the  end 
of  the  fourth  century  for  use  in  the  church,  viz.  the  DORIAN,  PHRYGIAN,  LYDIAN  and 
MIXOLYDIAN  (beginning  upon  D,  E,  F,  and  G  respectively);  and  two  centuries  later,  St. 
Gregory  the  Great  added  four  more,  i.e.  another  ser  es,  beginning  a  4th  below  the  others. 
The  first  series  was  known  as  that  of  the  Authentic  Modes,  and  the  second  one  as  that  of 
the  Plagal  Modes.1  Later  researches,  however,  have  made  this  statement  of  doubtful 
value.  An  example  of  the  manner  in  which  thesa  modes  are  harmonized  for  use  in  the 
Roman  Church,  in  the  book  mentioned  below,  is  here  given. 


*" ^    <»-     »      -<& -<&• 


^          P         &— 
i 


277.  These  modes  have  not  only  been  used  in  church  music  since  the  period  referred  to, 
but  have  been  employed  by  composers  of  secular  mu.--ic  to  obtain  distinctive  effects.  As 
(with  the  exception  of  the  one  licgmning  upon  I')  they  do  not  lend  themselves  to  treatment 
according  to  our  modern  harmonic  system,  they  can  l>c  appropriately  harmonized  l>cst  by  the 
use  of  triads,  with  occasional  chords  of  the  (5th  (i.e.  without  chords  of  the  7th).  and  do  not 
permit  our  authentic  cadence.  The  effect  produced  by  them  is  to  our  ears  something  antique: 
it  is  undoubtedly  because  of  the  refreshing  contrast  thus  obtained  that  composers  nre  now 
inclined  to  return  occasionally  to  their  use. 

278.  In  old  Gaelic,  Knglish,  Russian,  Polish  music,  etc.,  we  see  that  the  modes  also 
affected  the  popular  songs.  It  is,  therefore,  natural  that  some  of  the  examples  quoted  Inter 
should  be  found  in  the  works  of  e.g.  Chopin,  Tschaikowski,  Dvofak.  a.i  these  composers  were 
influenced  by  the  lolk  «onjr. 

1  For  a  thorough  discussion  of  the  subject,  the  student  i*  relerrcd  to  "I'lnin  Song  Accom- 
paniment," bv  Niedcrmcyer  and  d'Ortigue,  translated  by  Wallace  (ioodrich,  and  publmhed 
by  Novello,  I'.wer  <t  Co. 


250 


HARMONY 


179.   The  illustrations  given  are  in  the  following  modes.      (Observe  the  different  dis- 
tribution of  tones  and  semitones.)1 


Dorian. 


I'lirjuian. 


Lydian. 


Mixolydiau. 


.Kolian. 


GAELIC:  Tune,  "Martyrs"    (^olian,  with  B  for  starting  tone) 


Tune,  "St.  Davids" 
(Mixolydian,  with  D  for  starting  tone) 


etc. 


EARLY  ENGLISH 


Song,  "Cold  and  raw"    (  Dorian ) 


etc. 


Handel  employs  the  Dorian  mode  in  the  chorus  "And  1  will  exalt  him,"  ("Israel  in 
Egypt"), 


1  The  reader  is  referred  to  the  article  "  Musica  Ficta"  in  "Grove's  Dictionary."  In 
music  of  the  fifteenth  and  sixteenth  centuries,  the  natural  feeling  which  was  being  developed 
tor  what  we  now  call  the  leading-tone  caused  some  accidentals  to  be  written  in,  while  others 
were  supposed  to  be  supplied  by  the  singer  at  his  discretion,  so  that  some  of  the  old  modes 
were  thus  far  modified.  In  modern  music  we  sometimes  find  simply  a  partial  or  temporary 
use  of  an  old  mode  in  a  composition  written  in  other  respects  according  to  our  present  scale 
system,  (e.g.  Dvorak,  Quartet  Op.  96.) 


HARMONY 


iV.l 


and  has  taken  the  Phrygian  mode  for  the  first  measures  ol  the  fugue  "Egypt  was  glad  when 
they  departed,"  in  the  same  oratorio. 


.    J- 


In  Beethoven's  quartet  in  A  minor,  Op.  132,  one  movement  is  headed  "Song  of  Grati- 
tude, in  the  Lydian  mode,  offered  to  the  Divinity  by  a  Convalescent." 


^^      Adagio 


-9- — -=r 


bsj ^L: 

r 


etc. 


H 


This  mode  is  used  by  Chopin  in  his  Mazurka,  Op.  24,  No.  2. 


=1^-^^ 

^    •*•                        i    ^ 

->i  —  i  P  —  r—             *  n 

h  1^= 
R-*       f—  n- 

^=^---J  —  ^=*-4  !  —  fl 
*  f           f  * 

BRAHMS:  Symphony  in  E  Minor 


(Phrygian:  olinervo  the  Ix-autiful  change  to  our  modern  wale  of  F.  major  at  mrn»iirc3.) 

THCIIAIKOWSKI:  "  Koinco  ot  Jullfttf" 
( .-Kolian,  with  F  5  :m  xtartiiiK  t 


-T-/5.'  -  •*        +        *, 

•      »     T»  '     »     i  •      • 

'»    i  -  » 

' 


»  - 

rr  ---  ^  _____  ^L  —  __  i_      ,  __  '      i  *T-U—    . 

r  r 


252 


HARMONY 


DVORAK:  Symphony,  "From  the  New  World  " 
(JSolian,  with  £  for  starting  tone) 


f 


—  •   <t  ,» 


Japanese  National  Hymn.     (Dorian) 


HARMONY  OTHER  THAN  WITH  FOUR  VOICES 

280.  Through  natural  development,  and  from  custom,  harmony  in  four  parts  has  come 
to  be  considered  normal :  we  usually  have  a  quartet  of  voices,  a  quartet  of  stringed  instru- 
ments, a  quartet  of  wood-wind  instruments  in  the  orchestra,  etc.  It  will  now  be  well  for  the 
student  to  acquaint  himself  with  such  new  points  as  arise  when  more  or  less  than  four  voices 
are  used.  To  this  end  study  of  the  chapter  on  this  subject  in  Prout's  "  Harmony  "  is  recom- 
mended, and  the  following  works  will  repay  thorough  analysis  :  Bach,  "  St.  Matthew  Passion 
Music  ";  Brahms, "  Triumphlied  ";  Handel, "  Israel  in  Egypt ";  Hubert  Parry, "  De  Profundis  " 
(for  twelve  voices);  Strauss,  "Two  Anthems,"  Op.  34  (for  sixteen  voices);  instrumental 
sextets  and  octets  by  Mendelssohn,  Schubert,  and  Brahms. 


Page  35.        ADDITIONAL  EXERCISES 


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I1STDEX 


Accented  passing-tones,  138. 

Accidentals,  12,  13. 

^Eolian  mode,  42,  250. 

Altered  chords  (chromatically),  171. 

Anticipation,  221. 

Appoggiatura,  153,  219. 

Augmented  chords,  182. 

(Resolution  of),  183. 
Augmented  6  chord,  183. 
Augmented  6-4-3  chord,  186. 
Augmented  6-5  chord,  189. 
Augmented  intervals  and  skips,  5,  15,  39. 

(Allowable),  70,  121,  194. 
Augmented  triads,  38. 
Authentic  cadence,  66. 
Authentic  modes,  249. 
Auxiliary-tones,  78,  218. 


C  clefs,  152. 

Cadences,  66,  98. 

Changes  of  key  without  modulation,  234. 

Changing-tones,  219. 

Chords: 

Of  the  6th,  50.  53. 

Of  the  6th  (successive),  54. 

6-4,  49,  57. 

Of  the  7th,  71. 

(Their  resolution),  72. 

Dominant  7th,  72. 

(Its  regular  resolution),  75. 

(Its  irregular  resolutions),  93. 

Inversions  of  dominant  7th,  83. 

(Their  irregular  resolutions),  105. 

Leading-tone  7ths,  114. 

Diminished  7ths,  120. 
Secondary  7ths,  128. 
(Their  free  treatment),  129. 
(The  strict  rules),  132. 
(Their  resolutions),  133. 
Inversions  of  secondary  7ths,  142. 
Of  the  9th.  153. 
(Their  inversions),  161. 
Of  the  llth.  167. 
Of  the  13th.  169. 

Chromatically  altered  chords,  171. 
Augmented  chords,  182. 
Augments!  6th,  183. 
Augmented  6—4-3.  186. 
Augmented  6-5,  189. 


Chromatic  scale,  16. 

Circles  of  keys  (by  Sths),  13. 

Close  position,  20. 

Collateral  7ths,  128. 

Concealed  Sths  and  8ves,  47. 

Consecutive  Sths  and  8ves,  24,  134,  144. 

(When  permitted),  106,  190,  202. 

(Unison  followed  by  8ve  or  7th),  242. 
Consecutive  7ths  and  9ths,  160. 
Consonance,  7. 
Contrary  motion,  22. 
Cross  relation,  124,  239. 

D 

Deceptive  cadence,  68,  79,  98. 

Diatonic  scale,  3. 

Diminished  intervals,  5. 

Diminished  7th  (see  chord), 

Dissonance,  7. 

Dominant,  17. 

Dominant  7th,  9th,  llth,  13th  (see  chord). 

Dominant  relationship,  19,  231. 

Dorian  mode,  250. 

Doubling  of  tones  in: 

Leading-tone,  28,  70,  132. 
Triads,  20. 

Chords  of  6,  51,  53,  57. 
Chords  of  6-4,  57. 
Chords  of  dominant  7th,  73. 
Chords  of  leading-tone  7th,  1 17. 
Chords  of  diminished  7th.  121. 
Chords  of  secondary  7th,  133. 
Chords  of  9th,  154. 
Third  in  triads,  20,  41. 

Doubly    diminished    and    augmented     inter- 
vals, 6,  191. 
Drone  bass,  246. 

E 

Ecclesiastical  (see  modes). 
Enharmonic  notation,  2,  II,  9-1,  122,  175,  191, 

235. 
Eleventh,  167. 

F 

False  relation,  239. 

Fifth  (sw  roncenUvl.  ciTn«ecutive.  hidden). 
Fifths,  circles  of.  13. 
Figuration.  221. 
Figured  bam.  31. 

G 

Generator,  157. 
Greek  (see  modei). 


INDEX 


H 

Half-cadence,  67. 
Harmonising  triads,  36,  43. 
Heptatonic  scale,  3. 
Hidden  8ves  and  5  hs,  47. 

I 

Intervals,  1-10. 
Inversions  (see  chords). 
Inversion  of  intervals,  9. 
Inversion  of  triads,  49. 


Key  (circles  of  5ths),  13. 
(Changes  of),  234. 


Leading-tone,  12,  17,  28. 

Doubled,  36,  51.  70. 

7th  (see  chords). 
Leading  of  voices,  26. 
Lydian  mode,  250. 

M 

Major  intervals,  4. 
Major  scale,  3,  11. 
Me  liant,  17. 

Mediant  relationship,  231. 
Melodic  figuration,  221. 
Minor  scale,  11. 
Mixolydian  mode,  250. 
Modes  (Greek,  etc.),  249. 
Modulation,  43,  85,  227. 

(Table  of).  230. 
Motion  (similar,  etc.),  22. 


N 


Neapolitan  6th,  176. 
Ninth  (see  chords). 

O 

Oblique  (see  motion). 
Octaves,  consecutive,  23. 
Octaves,  hidden,  47,  74. 

(Unison,  the  same). 
Organ-point,  243. 

P 

Part-writing,  26. 
Passing-chords,  218. 
Passing-tones.  76,  138,  217. 
Pedal  (point),  243. 
Pentatonic  scale,  3. 
Perfect  intervals,  6. 
Phryirian  mode,  250. 
Picanlie,  Tierce  de,  42,  233. 
Plagal  cadence,  67. 


Plagal  modes,  249. 
Position  (close,  etc.),  20. 

R 

Relation  (cross),  124,  239. 
Relative  keys  (scales),  15,  38. 
Resolution,  8,  72. 

(See  chords). 
Retardation,  200. 
Root,  18. 
Rosalia,  70. 

S 
Scale: 

(See  chromatic,  diatonic,  heptatonic,  ma- 
jor, minor,  pentatonic,  relative). 
Semi-tone  (diatonic,  chromatic),  4. 
Sensitive  tones,  28. 
Sequences,  69. 
Seventh  (see  chords). 
Signature,  13. 
Similar  motion,  22. 
Sixth  (see  chords). 
Six-four  (see  chords). 

Sixth,  6-4-3,  6-5  augmented  (see  chords). 
Skips  (augmented),  39,  70,  121,  194. 

Subdominant,  17. 

Submediant,  17. 

Successive  chords  of  6th  (see  chords). 

Successive  chords  of  7th,  136. 

Supertonic,  17. 
Suspension: 

With  chords  of  9th,  153.     - 

Unprepared,  200. 

Dissonance  in,  202. 

Fourth  in,  202. 

Distinguished    from    preparation    of    7ths, 
203,  207. 

Resolution  delayed,  206. 


Tendency  tones,  17. 

Thirteenth  (see  chords). 

Three- voice  writing,  43,  65,  80,  89,  198. 

Tones  (see  auxiliary,  changing,  passing). 

Tierce  de  Picardie,  42,  233. 

Tonic,  17. 

Triads  (major),  18. 

Rules  for,  29. 

Rules  for  doubling,  20,  41. 

Harmonizing  soprano,  36. 
Triads  (minor),  38. 
Tritone,  30. 

U 

Unison  (see  octave). 
Unprepared  suspension,  200. 


89s 


OEC1? 
.1*3 


MUS-UB 

APR  1 1 1984 


'R  1 1 1984 


N 


MT50 


A     001  128667     1 


UNIVERSITY  of  CAUTORNU 

AT 
U>S  ANGELES 


